diff --git a/pytorch_lightning/metrics/functional/classification.py b/pytorch_lightning/metrics/functional/classification.py
index 527770b430..5a14aa22ed 100644
--- a/pytorch_lightning/metrics/functional/classification.py
+++ b/pytorch_lightning/metrics/functional/classification.py
@@ -312,7 +312,11 @@ def confusion_matrix(
     cm = bins.reshape(num_classes, num_classes).squeeze().float()
 
     if normalize:
-        cm = cm / cm.sum(-1)
+        cm = cm / cm.sum(-1, keepdim=True)
+        nan_elements = cm[torch.isnan(cm)].nelement()
+        if nan_elements != 0:
+            cm[torch.isnan(cm)] = 0
+            rank_zero_warn(f'{nan_elements} nan values found in confusion matrix have been replaced with zeros.')
 
     return cm
 
diff --git a/tests/metrics/functional/test_classification.py b/tests/metrics/functional/test_classification.py
index 8431846ba0..2074f70db5 100644
--- a/tests/metrics/functional/test_classification.py
+++ b/tests/metrics/functional/test_classification.py
@@ -187,6 +187,17 @@ def test_confusion_matrix():
     cm = confusion_matrix(pred, target, normalize=False, num_classes=3)
     assert torch.allclose(cm, torch.tensor([[5., 0., 0.], [0., 0., 0.], [0., 0., 0.]]))
 
+    # Example taken from https://scikit-learn.org/stable/auto_examples/model_selection/plot_confusion_matrix.html
+    target = torch.LongTensor([0] * 13 + [1] * 16 + [2] * 9)
+    pred = torch.LongTensor([0] * 13 + [1] * 10 + [2] * 15)
+    cm = confusion_matrix(pred, target, normalize=False, num_classes=3)
+    assert torch.allclose(cm, torch.tensor([[13., 0., 0.], [0., 10., 6.], [0., 0., 9.]]))
+    to_compare = cm / torch.tensor([[13.], [16.], [9.]])
+
+    cm = confusion_matrix(pred, target, normalize=True, num_classes=3)
+    assert torch.allclose(cm, to_compare)
+
+
 
 @pytest.mark.parametrize(['pred', 'target', 'expected_prec', 'expected_rec'], [
     pytest.param(torch.tensor([1., 0., 1., 0.]), torch.tensor([0., 1., 1., 0.]), [0.5, 0.5], [0.5, 0.5]),
diff --git a/tests/metrics/test_classification.py b/tests/metrics/test_classification.py
index fd6e1a3d1a..1be023b2af 100644
--- a/tests/metrics/test_classification.py
+++ b/tests/metrics/test_classification.py
@@ -53,6 +53,21 @@ def test_confusion_matrix(normalize, num_classes):
     assert isinstance(cm, torch.Tensor)
 
 
+@pytest.mark.parametrize(['normalize', 'num_classes'], [
+    pytest.param(True, 3)
+])
+def test_confusion_matrix_norm(normalize, num_classes):
+    """ test that user is warned if confusion matrix contains nans that are changed to zeros"""
+    conf_matrix = ConfusionMatrix(normalize=normalize, num_classes=num_classes)
+    assert conf_matrix.name == 'confusion_matrix'
+
+    with pytest.warns(UserWarning, match='6 nan values found in confusion matrix have been replaced with zeros.'):
+        target = torch.LongTensor([0] * 5)
+        pred = target.clone()
+        cm = conf_matrix(pred, target)
+        assert isinstance(cm, torch.Tensor)
+
+
 @pytest.mark.parametrize('pos_label', [1, 2.])
 def test_precision_recall(pos_label):
     pred, target = torch.tensor([1, 2, 3, 4]), torch.tensor([1, 0, 0, 1])