diff --git a/news/13790.bugfix.rst b/news/13790.bugfix.rst
new file mode 100644
index 00000000000..ee86424f168
--- /dev/null
+++ b/news/13790.bugfix.rst
@@ -0,0 +1 @@
+Improve the error message from ``pip config set`` when ``PIP_CONFIG_FILE`` points to a non-regular file (e.g. ``/dev/null``).
diff --git a/src/pip/_internal/configuration.py b/src/pip/_internal/configuration.py
index e164653bbc2..0816de012cc 100644
--- a/src/pip/_internal/configuration.py
+++ b/src/pip/_internal/configuration.py
@@ -378,9 +378,16 @@ def _get_parser_to_modify(self) -> tuple[str, RawConfigParser]:
         assert self.load_only
         parsers = self._parsers[self.load_only]
         if not parsers:
-            # This should not happen if everything works correctly.
+            env_config_file = os.environ.get("PIP_CONFIG_FILE")
+            if env_config_file and not os.path.isfile(env_config_file):
+                raise ConfigurationError(
+                    "Cannot modify pip configuration: "
+                    "PIP_CONFIG_FILE is not a regular file: "
+                    f"{env_config_file}"
+                )
+
             raise ConfigurationError(
-                "Fatal Internal error [id=2]. Please report as a bug."
+                "Cannot modify pip configuration: no configuration file is available."
             )
 
         # Use the highest priority parser.
diff --git a/tests/functional/test_configuration.py b/tests/functional/test_configuration.py
index b235212477a..3c8b8c6670e 100644
--- a/tests/functional/test_configuration.py
+++ b/tests/functional/test_configuration.py
@@ -216,6 +216,22 @@ def test_config_separated(
             result.stdout,
         )
 
+    def test_config_set_with_pip_config_file_devnull_shows_human_error(
+        self, script: PipTestEnvironment
+    ) -> None:
+        script.environ["PIP_CONFIG_FILE"] = os.devnull
+
+        result = script.pip(
+            "config",
+            "set",
+            "global.index-url",
+            "https://example.com/",
+            expect_error=True,
+        )
+        assert "Fatal Internal error [id=2]" not in result.stderr
+        assert "PIP_CONFIG_FILE" in result.stderr
+        assert "not a regular file" in result.stderr
+
     @pytest.mark.network
     def test_editable_mode_default_config(
         self, script: PipTestEnvironment, data: TestData