diff --git a/google/auth/_cloud_sdk.py b/google/auth/_cloud_sdk.py
index e772fe9..40e6aec 100644
--- a/google/auth/_cloud_sdk.py
+++ b/google/auth/_cloud_sdk.py
@@ -84,6 +84,13 @@
     return os.path.join(config_path, _CREDENTIALS_FILENAME)
 
 
+def _run_subprocess_ignore_stderr(command):
+    """ Return subprocess.check_output with the given command and ignores stderr."""
+    with open(os.devnull, "w") as devnull:
+        output = subprocess.check_output(command, stderr=devnull)
+    return output
+
+
 def get_project_id():
     """Gets the project ID from the Cloud SDK.
 
@@ -96,9 +103,9 @@
         command = _CLOUD_SDK_POSIX_COMMAND
 
     try:
-        output = subprocess.check_output(
-            (command,) + _CLOUD_SDK_CONFIG_COMMAND, stderr=subprocess.STDOUT
-        )
+        # Ignore the stderr coming from gcloud, so it won't be mixed into the output.
+        # https://github.com/googleapis/google-auth-library-python/issues/673
+        output = _run_subprocess_ignore_stderr((command,) + _CLOUD_SDK_CONFIG_COMMAND)
     except (subprocess.CalledProcessError, OSError, IOError):
         return None
 
diff --git a/tests/test__cloud_sdk.py b/tests/test__cloud_sdk.py
index 3377604..31cb6c2 100644
--- a/tests/test__cloud_sdk.py
+++ b/tests/test__cloud_sdk.py
@@ -71,6 +71,25 @@
     assert check_output.called
 
 
+def test__run_subprocess_ignore_stderr():
+    command = [
+        "python",
+        "-c",
+        "from __future__ import print_function;"
+        + "import sys;"
+        + "print('error', file=sys.stderr);"
+        + "print('output', file=sys.stdout)",
+    ]
+
+    # If we ignore stderr, then the output only has stdout
+    output = _cloud_sdk._run_subprocess_ignore_stderr(command)
+    assert output == b"output\n"
+
+    # If we pipe stderr to stdout, then the output is mixed with stdout and stderr.
+    output = subprocess.check_output(command, stderr=subprocess.STDOUT)
+    assert output == b"output\nerror\n" or output == b"error\noutput\n"
+
+
 @mock.patch("os.name", new="nt")
 def test_get_project_id_windows():
     check_output_patch = mock.patch(