diff --git a/tests/quantization/finegrained_fp8/test_fp8.py b/tests/quantization/finegrained_fp8/test_fp8.py
index e59c2068cde..69881b4cbbf 100644
--- a/tests/quantization/finegrained_fp8/test_fp8.py
+++ b/tests/quantization/finegrained_fp8/test_fp8.py
@@ -250,6 +250,10 @@ class FP8QuantizerTest(unittest.TestCase):
 class FP8LinearTest(unittest.TestCase):
     device = "cuda"
 
+    @unittest.skipIf(
+        torch.cuda.is_available() and torch.cuda.get_device_capability()[0] < 9,
+        "Skipping FP8LinearTest because it is not supported on GPU with capability < 9.0",
+    )
     def test_linear_preserves_shape(self):
         """
         Test that FP8Linear preserves shape when in_features == out_features.
@@ -262,6 +266,10 @@ class FP8LinearTest(unittest.TestCase):
         x_ = linear(x)
         self.assertEqual(x_.shape, x.shape)
 
+    @unittest.skipIf(
+        torch.cuda.is_available() and torch.cuda.get_device_capability()[0] < 9,
+        "Skipping FP8LinearTest because it is not supported on GPU with capability < 9.0",
+    )
     def test_linear_with_diff_feature_size_preserves_shape(self):
         """
         Test that FP8Linear generates the correct shape when in_features != out_features.