diff --git a/python/test/unit/hopper/test_experimental_tma.py b/python/test/unit/hopper/test_experimental_tma.py
index 7062093aef6d..23065953d65b 100644
--- a/python/test/unit/hopper/test_experimental_tma.py
+++ b/python/test/unit/hopper/test_experimental_tma.py
@@ -4,7 +4,7 @@
 import triton
 import triton.language as tl
 from triton.tools.experimental_descriptor import (create_1d_tma_descriptor, create_2d_tma_descriptor)
-from triton._internal_testing import dtypes_with_bfloat16, numpy_random, to_triton, requires_tma
+from triton._internal_testing import dtypes_with_bfloat16, numpy_random, to_triton, requires_tma, supports_tma, tma_skip_msg
 
 from typing import Optional
 
@@ -29,9 +29,11 @@ def unwrap_tensor(t: torch.Tensor | triton.runtime.jit.TensorWrapper):
 tma_dtypes = sorted(set(dtypes_with_bfloat16) - {"int64", "uint64", "float64"})
 
 
-@requires_tma
 @pytest.mark.parametrize("byval_tma", [True, False])
 def test_experimetal_descriptor_load(byval_tma):
+    if not supports_tma(byval_tma):
+        pytest.skip(tma_skip_msg(byval_tma))
+
     device = "cuda"
     SIZE = 128
 
@@ -82,11 +84,13 @@ def matmul_kernel_tma(a_desc_ptr, b_desc_ptr, c_desc_ptr,  #
     tl._experimental_descriptor_store(c_desc_ptr, accumulator, [offs_am, offs_bn])
 
 
-@requires_tma
 @pytest.mark.parametrize("num_stages", [1, 4])
 @pytest.mark.parametrize("BLOCK_M, BLOCK_N, BLOCK_K", [(32, 32, 32), (128, 64, 64), (128, 128, 64), (128, 256, 64)])
 @pytest.mark.parametrize("byval_tma", [True, False])
 def test_experimental_tma_matmul(num_stages, BLOCK_M, BLOCK_N, BLOCK_K, byval_tma):
+    if not supports_tma(byval_tma):
+        pytest.skip(tma_skip_msg(byval_tma))
+
     device = "cuda"
     M, N, K = 8192, 8192, 1024
     torch.manual_seed(42)
diff --git a/python/triton/_internal_testing.py b/python/triton/_internal_testing.py
index fa5df4f865d5..5ba0be1e34f9 100644
--- a/python/triton/_internal_testing.py
+++ b/python/triton/_internal_testing.py
@@ -4,6 +4,7 @@
 import torch
 import triton
 import triton.language as tl
+from triton.backends.nvidia.compiler import _path_to_binary
 import pytest
 
 from numpy.random import RandomState
@@ -140,8 +141,19 @@ def to_numpy(x):
         raise ValueError(f"Not a triton-compatible tensor: {x}")
 
 
-def supports_tma():
-    return is_cuda() and torch.cuda.get_device_capability()[0] >= 9
+def supports_tma(byval_only=False):
+    _, cuda_version = _path_to_binary("ptxas")
+    min_cuda_version = (12, 0) if byval_only else (12, 3)
+    cuda_version_tuple = tuple(map(int, cuda_version.split(".")))
+    assert len(cuda_version_tuple) == 2, cuda_version_tuple
+    return is_cuda() and torch.cuda.get_device_capability()[0] >= 9 and cuda_version_tuple >= min_cuda_version
+
+
+def tma_skip_msg(byval_only=False):
+    if byval_only:
+        return "Requires __grid_constant__ TMA support (NVIDIA Hopper or higher, CUDA 12.0 or higher)"
+    else:
+        return "Requires advanced TMA support (NVIDIA Hopper or higher, CUDA 12.3 or higher)"
 
 
-requires_tma = pytest.mark.skipif(not supports_tma(), reason="Requires TMA support (NVIDIA Hopper or higher)")
+requires_tma = pytest.mark.skipif(not supports_tma(), reason=tma_skip_msg())