diff --git a/test/optim/test_lrscheduler.py b/test/optim/test_lrscheduler.py
index 2671f5b7c93..b44eb9058c4 100644
--- a/test/optim/test_lrscheduler.py
+++ b/test/optim/test_lrscheduler.py
@@ -1837,6 +1837,15 @@ class TestLRScheduler(TestCase):
         )
         self._test(scheduler, targets, epochs)
 
+    def test_multiplicative_lr_with_lr_lambda(self):
+        lr_lambda = 0.95
+        with self.assertRaisesRegex(TypeError, "lr_lambda should be a function"):
+            MultiplicativeLR(self.opt, lr_lambda)
+
+        lr_lambda2 = 0.95
+        with self.assertRaisesRegex(TypeError, "lr_lambda should be a function"):
+            MultiplicativeLR(self.opt, [lr_lambda, lr_lambda2])
+
     @parametrize("T_mult", [1, 2, 4])
     def test_CosineAnnealingWarmRestarts_lr1(self, T_mult):
         iters = 100
diff --git a/torch/optim/lr_scheduler.py b/torch/optim/lr_scheduler.py
index 06ae24ef08d..8c553fb4901 100644
--- a/torch/optim/lr_scheduler.py
+++ b/torch/optim/lr_scheduler.py
@@ -398,6 +398,11 @@ class MultiplicativeLR(LRScheduler):
                     f"Expected {len(optimizer.param_groups)} lr_lambdas, but got {len(lr_lambda)}"
                 )
             self.lr_lambdas = list(lr_lambda)
+        for lr_lambda in self.lr_lambdas:
+            if not callable(lr_lambda):
+                raise TypeError(
+                    f"lr_lambda should be a function, but got {type(lr_lambda).__name__}"
+                )
         super().__init__(optimizer, last_epoch)
 
     @override