diff --git a/.eslintignore b/.eslintignore
index b260021d4..9d2200682 100644
--- a/.eslintignore
+++ b/.eslintignore
@@ -5,6 +5,7 @@ node_modules
 tests/files/malformed.js
 tests/files/with-syntax-error
 tests/files/just-json-files/invalid.json
+tests/files/typescript-d-ts/
 resolvers/webpack/test/files
 # we want to ignore "tests/files" here, but unfortunately doing so would
 # interfere with unit test and fail it for some reason.
diff --git a/CHANGELOG.md b/CHANGELOG.md
index 9b4cb5608..987da7fb6 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -24,6 +24,7 @@ This change log adheres to standards from [Keep a CHANGELOG](http://keepachangel
 - [`namespace`]/`ExportMap`: Fix interface declarations for TypeScript ([#1764], thanks [@julien1619])
 - [`no-unused-modules`]: avoid order-dependence ([#1744], thanks [@darkartur])
 - [`no-internal-modules`]: also check `export from` syntax ([#1691], thanks [@adjerbetian])
+- TypeScript: [`export`]: avoid a crash with `export =` ([#1801], thanks [@ljharb])
 
 ### Changed
 - [Refactor] `no-extraneous-dependencies`: use moduleVisitor ([#1735], thanks [@adamborowski])
@@ -690,6 +691,7 @@ for info on changes for earlier releases.
 [`memo-parser`]: ./memo-parser/README.md
 
 [#1802]: https://github.com/benmosher/eslint-plugin-import/pull/1802
+[#1801]: https://github.com/benmosher/eslint-plugin-import/issues/1801
 [#1788]: https://github.com/benmosher/eslint-plugin-import/pull/1788
 [#1786]: https://github.com/benmosher/eslint-plugin-import/pull/1786
 [#1785]: https://github.com/benmosher/eslint-plugin-import/pull/1785
diff --git a/src/ExportMap.js b/src/ExportMap.js
index d72952ef4..dfd9ca155 100644
--- a/src/ExportMap.js
+++ b/src/ExportMap.js
@@ -590,7 +590,9 @@ ExportMap.parse = function (path, content, context) {
                 moduleBlockNode.declaration :
                 moduleBlockNode
 
-              if (namespaceDecl.type === 'VariableDeclaration') {
+              if (!namespaceDecl) {
+                // TypeScript can check this for us; we needn't
+              } else if (namespaceDecl.type === 'VariableDeclaration') {
                 namespaceDecl.declarations.forEach((d) =>
                   recursivePatternCapture(d.id, (id) => m.namespace.set(
                     id.name,
diff --git a/tests/files/typescript-d-ts/.eslintrc b/tests/files/typescript-d-ts/.eslintrc
new file mode 100644
index 000000000..f22e9cb62
--- /dev/null
+++ b/tests/files/typescript-d-ts/.eslintrc
@@ -0,0 +1,12 @@
+{
+  "overrides": [
+    {
+      "files": "**.ts",
+      "parser": "@typescript-eslint/parser",
+      "extends": "../../../config/typescript",
+      "rules": {
+        "import/export": "error",
+      },
+    },
+  ],
+}
diff --git a/tests/files/typescript-d-ts/file1.ts b/tests/files/typescript-d-ts/file1.ts
new file mode 100644
index 000000000..872c30e8a
--- /dev/null
+++ b/tests/files/typescript-d-ts/file1.ts
@@ -0,0 +1,6 @@
+declare namespace ts {
+  const x: string;
+  export { x };
+}
+
+export = ts;
diff --git a/tests/files/typescript-d-ts/file2.ts b/tests/files/typescript-d-ts/file2.ts
new file mode 100644
index 000000000..e8ed5afca
--- /dev/null
+++ b/tests/files/typescript-d-ts/file2.ts
@@ -0,0 +1 @@
+export * from './file1.ts'
diff --git a/tests/src/cli.js b/tests/src/cli.js
index 53d6e8fdc..5e0a74e36 100644
--- a/tests/src/cli.js
+++ b/tests/src/cli.js
@@ -22,7 +22,7 @@ describe('CLI regression tests', function () {
       })
     })
     it("doesn't throw an error on gratuitous, erroneous self-reference", function () {
-      expect(() => cli.executeOnFiles(['./tests/files/issue210.js'])).not.to.throw(Error)
+      expect(() => cli.executeOnFiles(['./tests/files/issue210.js'])).not.to.throw()
     })
   })
 
@@ -41,7 +41,7 @@ describe('CLI regression tests', function () {
       }
     })
 
-    it('throws an error on invalid JSON', function () {
+    it('throws an error on invalid JSON', () => {
       const invalidJSON = './tests/files/just-json-files/invalid.json'
       const results = cli.executeOnFiles([invalidJSON])
       expect(results).to.eql({
diff --git a/tests/src/rules/export.js b/tests/src/rules/export.js
index 76fae4567..fb301495e 100644
--- a/tests/src/rules/export.js
+++ b/tests/src/rules/export.js
@@ -1,4 +1,4 @@
-import { test, SYNTAX_CASES, getTSParsers } from '../utils'
+import { test, testFilePath, SYNTAX_CASES, getTSParsers } from '../utils'
 
 import { RuleTester } from 'eslint'
 
@@ -187,6 +187,10 @@ context('TypeScript', function () {
             }
           `,
         }, parserConfig)),
+        test(Object.assign({
+          code: 'export * from "./file1.ts"',
+          filename: testFilePath('typescript-d-ts/file-2.ts'),
+        }, parserConfig)),
       ],
       invalid: [
         // type/value name clash