diff --git a/noxfile.py b/noxfile.py
index 49ec38f6..2b973857 100644
--- a/noxfile.py
+++ b/noxfile.py
@@ -256,6 +256,7 @@ def system(session):
 
     install_systemtest_dependencies(session, "-c", constraints_path)
 
+    # Print out package versions.
     session.run("python", "-m", "pip", "freeze")
 
     # Run py.test against the system tests.
@@ -352,12 +353,15 @@ def prerelease(session):
         "--quiet",
         f"--junitxml=prerelease_unit_{session.python}_sponge_log.xml",
         os.path.join("tests", "unit"),
+        *session.posargs,
     )
+
     session.run(
         "py.test",
         "--quiet",
         f"--junitxml=prerelease_system_{session.python}_sponge_log.xml",
         os.path.join("tests", "system"),
+        *session.posargs,
     )
 
 
@@ -515,7 +519,9 @@ def prerelease_deps(session):
     session.install(*other_deps)
     session.run("python", "-m", "pip", "freeze")
 
-    # Print out prerelease package versions
+    # Print out package versions.
+    session.run("python", "-m", "pip", "freeze")
+
     session.run(
         "python", "-c", "import google.protobuf; print(google.protobuf.__version__)"
     )
diff --git a/pandas_gbq/gbq.py b/pandas_gbq/gbq.py
index f93999a9..60bb8bda 100644
--- a/pandas_gbq/gbq.py
+++ b/pandas_gbq/gbq.py
@@ -411,7 +411,20 @@ def run_query(self, query, max_results=None, progress_bar_type=None, **kwargs):
         timeout_ms = job_config_dict.get("jobTimeoutMs") or job_config_dict[
             "query"
         ].get("timeoutMs")
-        timeout_ms = int(timeout_ms) if timeout_ms else None
+
+        if timeout_ms:
+            timeout_ms = int(timeout_ms)
+            # Having too small a timeout_ms results in individual
+            # API calls timing out before they can finish.
+            # ~300 milliseconds is rule of thumb for bare minimum
+            # latency from the BigQuery API.
+            minimum_latency = 400
+            if timeout_ms < minimum_latency:
+                raise QueryTimeout(
+                    f"Query timeout must be at least 400 milliseconds: timeout_ms equals {timeout_ms}."
+                )
+        else:
+            timeout_ms = None
 
         self._start_timer()
         job_config = bigquery.QueryJobConfig.from_api_repr(job_config_dict)
diff --git a/tests/system/test_gbq.py b/tests/system/test_gbq.py
index 7afa4ae9..9bbefceb 100644
--- a/tests/system/test_gbq.py
+++ b/tests/system/test_gbq.py
@@ -473,13 +473,41 @@ def test_timeout_configuration(self, project_id):
         sql_statement = """
         select count(*) from unnest(generate_array(1,1000000)), unnest(generate_array(1, 10000))
         """
+
+        # This first test confirms that we get a timeout error if we exceed the timeout limit.
+        # The above query is expected to take a long time and exceed the limit.
         configs = [
+            # we have a minimum limit on the timeout_ms being 400 milliseconds
+            # see pandas-gbq/gbq.py/GbqConnector/run_query docstring
+            # for more details.
             # pandas-gbq timeout configuration. Transformed to REST API compatible version.
-            {"query": {"useQueryCache": False, "timeoutMs": 1}},
+            {"query": {"useQueryCache": False, "timeoutMs": 401}},
             # REST API job timeout. See:
             # https://cloud.google.com/bigquery/docs/reference/rest/v2/Job#JobConfiguration.FIELDS.job_timeout_ms
+            {"query": {"useQueryCache": False}, "jobTimeoutMs": 401},
+        ]
+        for config in configs:
+            with pytest.raises(gbq.QueryTimeout):
+                gbq.read_gbq(
+                    sql_statement,
+                    project_id=project_id,
+                    credentials=self.credentials,
+                    configuration=config,
+                )
+
+        # This second test confirms out our validation logic won't allow a
+        # value less than or equal to 400 be used as a timeout value.
+        # by exercising the system for various edge cases to ensure we catch
+        # invalid values less than or equal to 400.
+        configs = [
+            {"query": {"useQueryCache": False, "timeoutMs": 399}},
+            {"query": {"useQueryCache": False, "timeoutMs": 400}},
+            {"query": {"useQueryCache": False, "timeoutMs": 1}},
+            {"query": {"useQueryCache": False}, "jobTimeoutMs": 399},
+            {"query": {"useQueryCache": False}, "jobTimeoutMs": 400},
             {"query": {"useQueryCache": False}, "jobTimeoutMs": 1},
         ]
+
         for config in configs:
             with pytest.raises(gbq.QueryTimeout):
                 gbq.read_gbq(