diff --git a/sklearn/cluster/_kmeans.py b/sklearn/cluster/_kmeans.py
index 8b24be6ace987..07a3496517f1a 100644
--- a/sklearn/cluster/_kmeans.py
+++ b/sklearn/cluster/_kmeans.py
@@ -1057,7 +1057,9 @@ def fit(self, X, y=None, sample_weight=None):
                 x_squared_norms=x_squared_norms, n_threads=self._n_threads)
 
             # determine if these results are the best so far
-            if best_inertia is None or inertia < best_inertia:
+            # allow small tolerance on the inertia to accommodate for
+            # non-deterministic rounding errors due to parallel computation
+            if best_inertia is None or inertia < best_inertia * (1 - 1e-6):
                 best_labels = labels
                 best_centers = centers
                 best_inertia = inertia