diff --git a/news/7269.bugfix.rst b/news/7269.bugfix.rst
new file mode 100644
index 00000000000..6fb4ba3af65
--- /dev/null
+++ b/news/7269.bugfix.rst
@@ -0,0 +1,3 @@
+Ignore ``.dist-info`` directories if the stem is not a valid Python distribution
+name. These are not usable as installation metadata anyway, and excluding them
+prevents their contents from causing cryptic errors in other parts of pip.
diff --git a/src/pip/_internal/metadata/base.py b/src/pip/_internal/metadata/base.py
index 724b0c04494..895cabef29f 100644
--- a/src/pip/_internal/metadata/base.py
+++ b/src/pip/_internal/metadata/base.py
@@ -1,3 +1,5 @@
+import logging
+import re
 from typing import Container, Iterator, List, Optional
 
 from pip._vendor.packaging.version import _BaseVersion
@@ -5,7 +7,21 @@
 from pip._internal.utils.misc import stdlib_pkgs  # TODO: Move definition here.
 
 
+logger = logging.getLogger(__name__)
+
+
 class BaseDistribution:
+    @property
+    def location(self):
+        # type: () -> Optional[str]
+        """Where the distribution is loaded from.
+
+        A string value is not necessarily a filesystem path, since distributions
+        can be loaded from other sources, e.g. arbitrary zip archives. ``None``
+        means the distribution is created in-memory.
+        """
+        raise NotImplementedError()
+
     @property
     def metadata_version(self):
         # type: () -> Optional[str]
@@ -61,10 +77,37 @@ def get_distribution(self, name):
         """Given a requirement name, return the installed distributions."""
         raise NotImplementedError()
 
+    def _iter_distributions(self):
+        # type: () -> Iterator[BaseDistribution]
+        """Iterate through installed distributions.
+
+        This function should be implemented by subclass, but never called
+        directly. Use the public ``iter_distribution()`` instead, which
+        implements additional logic to make sure the distributions are valid.
+        """
+        raise NotImplementedError()
+
     def iter_distributions(self):
         # type: () -> Iterator[BaseDistribution]
         """Iterate through installed distributions."""
-        raise NotImplementedError()
+        for dist in self._iter_distributions():
+            # Make sure the distribution actually comes from a valid Python
+            # packaging distribution. Pip's AdjacentTempDirectory leaves folders
+            # e.g. ``~atplotlib.dist-info`` if cleanup was interrupted. The
+            # valid project name pattern is taken from PEP 508.
+            project_name_valid = re.match(
+                r"^([A-Z0-9]|[A-Z0-9][A-Z0-9._-]*[A-Z0-9])$",
+                dist.canonical_name,
+                flags=re.IGNORECASE,
+            )
+            if not project_name_valid:
+                logger.warning(
+                    "Ignoring invalid distribution %s (%s)",
+                    dist.canonical_name,
+                    dist.location,
+                )
+                continue
+            yield dist
 
     def iter_installed_distributions(
         self,
diff --git a/src/pip/_internal/metadata/pkg_resources.py b/src/pip/_internal/metadata/pkg_resources.py
index d2fb29e2e9a..5cd9eaee641 100644
--- a/src/pip/_internal/metadata/pkg_resources.py
+++ b/src/pip/_internal/metadata/pkg_resources.py
@@ -24,6 +24,11 @@ def from_wheel(cls, path, name):
             dist = pkg_resources_distribution_for_wheel(zf, name, path)
         return cls(dist)
 
+    @property
+    def location(self):
+        # type: () -> Optional[str]
+        return self._dist.location
+
     @property
     def metadata_version(self):
         # type: () -> Optional[str]
@@ -115,7 +120,7 @@ def get_distribution(self, name):
             return None
         return self._search_distribution(name)
 
-    def iter_distributions(self):
+    def _iter_distributions(self):
         # type: () -> Iterator[BaseDistribution]
         for dist in self._ws:
             yield Distribution(dist)
diff --git a/tests/functional/test_freeze.py b/tests/functional/test_freeze.py
index 4fd91b5d8e5..dbda48a92b4 100644
--- a/tests/functional/test_freeze.py
+++ b/tests/functional/test_freeze.py
@@ -5,6 +5,7 @@
 from doctest import ELLIPSIS, OutputChecker
 
 import pytest
+from packaging.utils import canonicalize_name
 
 from tests.lib import (
     _create_test_package,
@@ -128,26 +129,23 @@ def fake_install(pkgname, dest):
     )
     for pkgname in valid_pkgnames + invalid_pkgnames:
         fake_install(pkgname, script.site_packages_path)
+
     result = script.pip('freeze', expect_stderr=True)
-    for pkgname in valid_pkgnames:
-        _check_output(
-            result.stdout,
-            '...{}==1.0...'.format(pkgname.replace('_', '-'))
-        )
-    for pkgname in invalid_pkgnames:
-        # Check that the full distribution repr is present.
-        dist_repr = '{} 1.0 ('.format(pkgname.replace('_', '-'))
-        expected = (
-            '...Could not generate requirement for '
-            'distribution {}...'.format(dist_repr)
-        )
-        _check_output(result.stderr, expected)
 
-    # Also check that the parse error details occur at least once.
-    # We only need to find one occurrence to know that exception details
-    # are logged.
-    expected = '...site-packages): Parse error at "...'
-    _check_output(result.stderr, expected)
+    # Check all valid names are in the output.
+    output_lines = {line.strip() for line in result.stdout.splitlines()}
+    for name in valid_pkgnames:
+        f"{canonicalize_name(name)}==1.0" in output_lines
+
+    # Check all invalid names are excluded from the output.
+    canonical_invalid_names = {canonicalize_name(n) for n in invalid_pkgnames}
+    for line in output_lines:
+        output_name, _, _ = line.partition("=")
+        assert canonicalize_name(output_name) not in canonical_invalid_names
+
+    # The invalid names should be logged.
+    for name in canonical_invalid_names:
+        assert f"Ignoring invalid distribution {name} (" in result.stderr
 
 
 @pytest.mark.git