diff --git a/news/8288.removal b/news/8288.removal
new file mode 100644
index 00000000000..830d91aab95
--- /dev/null
+++ b/news/8288.removal
@@ -0,0 +1 @@
+Add deprecation warning for invalid requirements format "base>=1.0[extra]"
diff --git a/src/pip/_internal/req/constructors.py b/src/pip/_internal/req/constructors.py
index 7ca3370110f..43b7324462b 100644
--- a/src/pip/_internal/req/constructors.py
+++ b/src/pip/_internal/req/constructors.py
@@ -23,6 +23,7 @@
 from pip._internal.models.wheel import Wheel
 from pip._internal.pyproject import make_pyproject_path
 from pip._internal.req.req_install import InstallRequirement
+from pip._internal.utils.deprecation import deprecated
 from pip._internal.utils.filetypes import ARCHIVE_EXTENSIONS
 from pip._internal.utils.misc import is_installable_dir, splitext
 from pip._internal.utils.typing import MYPY_CHECK_RUNNING
@@ -368,6 +369,14 @@ def with_source(text):
             if add_msg:
                 msg += '\nHint: {}'.format(add_msg)
             raise InstallationError(msg)
+        else:
+            # Check that specifiers are PEP-440 compliant
+            for spec in req.specifier:
+                if not isinstance(spec, Specifier):
+                    msg = "Invalid version specifier '{}'".format(str(spec))
+                    replace = ("using PEP 440-compatible specifiers. "
+                               "https://www.python.org/dev/peps/pep-0440")
+                    deprecated(msg, replacement=replace, gone_in="21.0")
     else:
         req = None
 
diff --git a/tests/functional/test_new_resolver.py b/tests/functional/test_new_resolver.py
index 4874874e788..74aa1bddd80 100644
--- a/tests/functional/test_new_resolver.py
+++ b/tests/functional/test_new_resolver.py
@@ -200,8 +200,6 @@ def test_new_resolver_ignore_dependencies(script):
     [
         "base[add]",
         "base[add] >= 0.1.0",
-        # Non-standard syntax. To deprecate, see pypa/pip#8288.
-        "base >= 0.1.0[add]",
     ],
 )
 def test_new_resolver_installs_extras(tmpdir, script, root_dep):
@@ -228,6 +226,32 @@ def test_new_resolver_installs_extras(tmpdir, script, root_dep):
     assert_installed(script, base="0.1.0", dep="0.1.0")
 
 
+def test_new_resolver_installs_extras_deprecated(tmpdir, script):
+    req_file = tmpdir.joinpath("requirements.txt")
+    req_file.write_text("base >= 0.1.0[add]")
+
+    create_basic_wheel_for_package(
+        script,
+        "base",
+        "0.1.0",
+        extras={"add": ["dep"]},
+    )
+    create_basic_wheel_for_package(
+        script,
+        "dep",
+        "0.1.0",
+    )
+    result = script.pip(
+        "install", "--unstable-feature=resolver",
+        "--no-cache-dir", "--no-index",
+        "--find-links", script.scratch_path,
+        "-r", req_file,
+        expect_stderr=True
+    )
+    assert "DEPRECATION: Invalid version specifier" in result.stderr
+    assert_installed(script, base="0.1.0", dep="0.1.0")
+
+
 def test_new_resolver_installs_extras_warn_missing(script):
     create_basic_wheel_for_package(
         script,