diff --git a/src/components/selectable/selectable_templates/__snapshots__/selectable_template_sitewide.test.tsx.snap b/src/components/selectable/selectable_templates/__snapshots__/selectable_template_sitewide.test.tsx.snap
index fe816f28dfd..290e89d5692 100644
--- a/src/components/selectable/selectable_templates/__snapshots__/selectable_template_sitewide.test.tsx.snap
+++ b/src/components/selectable/selectable_templates/__snapshots__/selectable_template_sitewide.test.tsx.snap
@@ -51,56 +51,6 @@ exports[`EuiSelectableTemplateSitewide is rendered 1`] = `
 </div>
 `;
 
-exports[`EuiSelectableTemplateSitewide props popoverButton is not rendered with popoverButtonBreakpoints xs 1`] = `
-<div
-  class="euiSelectable euiSelectableTemplateSitewide"
->
-  <div
-    class="euiPopover emotion-euiPopover-block"
-  >
-    <div
-      class="euiFormControlLayout euiFormControlLayout--fullWidth"
-    >
-      <div
-        class="euiFormControlLayout__childrenWrapper"
-      >
-        <div
-          class="euiFormControlLayoutIcons euiFormControlLayoutIcons--left euiFormControlLayoutIcons--absolute"
-        >
-          <span
-            class="euiFormControlLayoutCustomIcon"
-          >
-            <span
-              aria-hidden="true"
-              class="euiFormControlLayoutCustomIcon__icon"
-              data-euiicon-type="search"
-            />
-          </span>
-        </div>
-        <input
-          aria-activedescendant=""
-          aria-describedby="generated-id_instructions"
-          aria-haspopup="listbox"
-          aria-label="Filter options"
-          autocomplete="off"
-          class="euiFieldSearch euiFieldSearch--fullWidth euiSelectableSearch euiSelectableTemplateSitewide__search"
-          placeholder="Search for anything..."
-          type="search"
-          value=""
-        />
-      </div>
-    </div>
-    <p
-      class="emotion-euiScreenReaderOnly"
-      id="generated-id_instructions"
-    >
-       
-      Use the Up and Down arrow keys to move focus over options. Press Enter to select. Press Escape to collapse options.
-    </p>
-  </div>
-</div>
-`;
-
 exports[`EuiSelectableTemplateSitewide props popoverButton is rendered 1`] = `
 <div
   class="euiSelectable euiSelectableTemplateSitewide"
@@ -108,23 +58,15 @@ exports[`EuiSelectableTemplateSitewide props popoverButton is rendered 1`] = `
   <div
     class="euiPopover emotion-euiPopover-inline-block"
   >
-    <button>
-      Button
-    </button>
-  </div>
-</div>
-`;
-
-exports[`EuiSelectableTemplateSitewide props popoverButton is rendered with popoverButtonBreakpoints m 1`] = `
-<div
-  class="euiSelectable euiSelectableTemplateSitewide"
->
-  <div
-    class="euiPopover emotion-euiPopover-inline-block"
-  >
-    <button>
-      Button
-    </button>
+    <span
+      class="euiSelectableTemplateSitewide__popoverTrigger"
+    >
+      <button
+        data-test-subj="mobilePopoverButton"
+      >
+        Button
+      </button>
+    </span>
   </div>
 </div>
 `;
diff --git a/src/components/selectable/selectable_templates/selectable_template_sitewide.test.tsx b/src/components/selectable/selectable_templates/selectable_template_sitewide.test.tsx
index a5a6be21213..075e143f4f2 100644
--- a/src/components/selectable/selectable_templates/selectable_template_sitewide.test.tsx
+++ b/src/components/selectable/selectable_templates/selectable_template_sitewide.test.tsx
@@ -7,9 +7,11 @@
  */
 
 import React from 'react';
+import { fireEvent } from '@testing-library/react';
+import userEvent from '@testing-library/user-event';
+import { render, waitForEuiPopoverOpen } from '../../../test/rtl';
 import { shouldRenderCustomStyles } from '../../../test/internal';
 import { requiredProps } from '../../../test/required_props';
-import { render } from '../../../test/rtl';
 
 import { EuiSelectableTemplateSitewide } from './selectable_template_sitewide';
 import { EuiSelectableTemplateSitewideOption } from './selectable_template_sitewide_option';
@@ -127,11 +129,15 @@ describe('EuiSelectableTemplateSitewide', () => {
       beforeAll(() => (window.innerWidth = 670));
       afterAll(() => 1024); // reset to jsdom's default
 
+      const button = (
+        <button data-test-subj="mobilePopoverButton">Button</button>
+      );
+
       test('is rendered', () => {
         const { container } = render(
           <EuiSelectableTemplateSitewide
             options={options}
-            popoverButton={<button>Button</button>}
+            popoverButton={button}
           />
         );
 
@@ -139,27 +145,57 @@ describe('EuiSelectableTemplateSitewide', () => {
       });
 
       test('is rendered with popoverButtonBreakpoints m', () => {
-        const { container } = render(
+        const { getByTestSubject } = render(
           <EuiSelectableTemplateSitewide
             options={options}
-            popoverButton={<button>Button</button>}
+            popoverButton={button}
             popoverButtonBreakpoints={['xs', 's', 'm']}
           />
         );
 
-        expect(container.firstChild).toMatchSnapshot();
+        expect(getByTestSubject('mobilePopoverButton')).toBeInTheDocument();
       });
 
       test('is not rendered with popoverButtonBreakpoints xs', () => {
-        const { container } = render(
+        const { queryByTestSubject } = render(
           <EuiSelectableTemplateSitewide
             options={options}
-            popoverButton={<button>Button</button>}
+            popoverButton={button}
             popoverButtonBreakpoints={['xs']}
           />
         );
 
-        expect(container.firstChild).toMatchSnapshot();
+        expect(
+          queryByTestSubject('mobilePopoverButton')
+        ).not.toBeInTheDocument();
+      });
+
+      test('toggles the selectable popover for keyboard users', () => {
+        const { getByTestSubject } = render(
+          <EuiSelectableTemplateSitewide
+            options={options}
+            popoverButton={<div>{button}</div>}
+          />
+        );
+        // fireEvent doesn't seem to work: https://github.com/testing-library/user-event/issues/179#issuecomment-1125146667
+        getByTestSubject('mobilePopoverButton').focus();
+        userEvent.keyboard('{enter}');
+        waitForEuiPopoverOpen();
+
+        expect(getByTestSubject('euiSelectableList')).toBeInTheDocument();
+      });
+
+      test('toggles the selectable popover even when a wrapper exists around the button', () => {
+        const { getByTestSubject } = render(
+          <EuiSelectableTemplateSitewide
+            options={options}
+            popoverButton={<>{button}</>}
+          />
+        );
+        fireEvent.click(getByTestSubject('mobilePopoverButton'));
+        waitForEuiPopoverOpen();
+
+        expect(getByTestSubject('euiSelectableList')).toBeInTheDocument();
       });
     });
   });
diff --git a/src/components/selectable/selectable_templates/selectable_template_sitewide.tsx b/src/components/selectable/selectable_templates/selectable_template_sitewide.tsx
index 64b0e0293fb..eaabd225c02 100644
--- a/src/components/selectable/selectable_templates/selectable_template_sitewide.tsx
+++ b/src/components/selectable/selectable_templates/selectable_template_sitewide.tsx
@@ -11,6 +11,7 @@ import React, {
   ReactNode,
   useState,
   useMemo,
+  useCallback,
   CSSProperties,
   ReactElement,
 } from 'react';
@@ -106,9 +107,9 @@ export const EuiSelectableTemplateSitewide: FunctionComponent<
     _closePopover && _closePopover();
   };
 
-  const togglePopover = () => {
-    setPopoverIsOpen(!popoverIsOpen);
-  };
+  const togglePopover = useCallback(() => {
+    setPopoverIsOpen((isOpen) => !isOpen);
+  }, []);
 
   // Width applied to the internal div
   const popoverWidth: CSSProperties['width'] = width || 600;
@@ -195,17 +196,18 @@ export const EuiSelectableTemplateSitewide: FunctionComponent<
     return popoverButtonBreakpoints.includes(currentBreakpoint);
   }, [currentBreakpoint, popoverButtonBreakpoints]);
 
-  let popoverTrigger: ReactElement;
-  if (popoverButton && canShowPopoverButton) {
-    popoverTrigger = React.cloneElement(popoverButton, {
-      ...popoverButton.props,
-      onClick: togglePopover,
-      onKeyDown: (e: KeyboardEvent) => {
-        // Selectable preventsDefault on Enter which kills browser controls for pressing the button
-        e.stopPropagation();
-      },
-    });
-  }
+  const popoverTrigger = useMemo(() => {
+    if (!popoverButton || !canShowPopoverButton) return;
+    return (
+      <span
+        className="euiSelectableTemplateSitewide__popoverTrigger"
+        onClick={togglePopover}
+        onKeyDown={(e) => e.stopPropagation()}
+      >
+        {popoverButton}
+      </span>
+    );
+  }, [popoverButton, canShowPopoverButton, togglePopover]);
 
   return (
     <EuiSelectable
diff --git a/upcoming_changelogs/7339.md b/upcoming_changelogs/7339.md
new file mode 100644
index 00000000000..c6d7160793b
--- /dev/null
+++ b/upcoming_changelogs/7339.md
@@ -0,0 +1,3 @@
+**Bug fixes**
+
+- Fixed an `EuiSelectableTemplateSitewide` bug where the `popoverButton` behavior would break if passed a non-DOM React wrapper