diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/compute_normal.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/compute_normal.h
index 8a9d9847f7b..e3d52c2bcef 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/compute_normal.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/compute_normal.h
@@ -49,7 +49,12 @@ namespace internal {
   {
     typename GT::FT norm = CGAL::approximate_sqrt(
         traits.compute_squared_length_3_object()(v));
-    v = traits.construct_divided_vector_3_object()(v, norm);
+    //If the vector is small enough, approx_sqrt might return 0, and then we get nan values. 
+    //To avoid that, we check the resulted norm. If it is 0, we don't normalize.
+    if(norm != 0)
+    {
+      v = traits.construct_divided_vector_3_object()(v, norm );
+    }
   }
 
   template<typename Point