diff --git a/pytorch_lightning/loggers/mlflow.py b/pytorch_lightning/loggers/mlflow.py
index de915785dcb45..ee9f8f86cf247 100644
--- a/pytorch_lightning/loggers/mlflow.py
+++ b/pytorch_lightning/loggers/mlflow.py
@@ -16,6 +16,8 @@
 MLflow
 ------
 """
+import re
+import warnings
 from argparse import Namespace
 from time import time
 from typing import Any, Dict, Optional, Union
@@ -151,6 +153,13 @@ def log_metrics(self, metrics: Dict[str, float], step: Optional[int] = None) ->
             if isinstance(v, str):
                 log.warning(f'Discarding metric with string value {k}={v}.')
                 continue
+
+            new_k = re.sub("[^a-zA-Z0-9_/. -]+", "", k)
+            if k != new_k:
+                warnings.warn(("MLFlow only allows '_', '/', '.' and ' ' special characters in metric name.\n",
+                               f"Replacing {k} with {new_k}."))
+            k = new_k
+
             self.experiment.log_metric(self.run_id, k, v, timestamp_ms, step)
 
     @rank_zero_only
diff --git a/tests/loggers/test_mlflow.py b/tests/loggers/test_mlflow.py
index db2c353dc4e2c..618f0ffe60903 100644
--- a/tests/loggers/test_mlflow.py
+++ b/tests/loggers/test_mlflow.py
@@ -137,7 +137,8 @@ def test_mlflow_logger_dirs_creation(tmpdir):
         assert set(os.listdir(tmpdir / exp_id)) == {run_id, 'meta.yaml'}
 
     model = EvalModelTemplate()
-    trainer = Trainer(default_root_dir=tmpdir, logger=logger, max_epochs=1, limit_val_batches=3)
+    trainer = Trainer(default_root_dir=tmpdir, logger=logger, max_epochs=1, limit_val_batches=3,
+                      log_gpu_memory=True)
     trainer.fit(model)
     assert set(os.listdir(tmpdir / exp_id)) == {run_id, 'meta.yaml'}
     assert 'epoch' in os.listdir(tmpdir / exp_id / run_id / 'metrics')