diff --git a/src/zarr/codecs/sharding.py b/src/zarr/codecs/sharding.py
index 609e32f87d..d0b2cec285 100644
--- a/src/zarr/codecs/sharding.py
+++ b/src/zarr/codecs/sharding.py
@@ -171,6 +171,16 @@ def get_chunk_slices_vectorized(
         valid : ndarray of shape (n_chunks,)
             Boolean mask indicating which chunks are non-empty.
         """
+        # Handle 0-dimensional arrays (n_dims == 0)
+        if chunk_coords_array.shape[1] == 0:
+            # offsets_and_lengths has shape (2,) for 0D, reshape to (1, 2)
+            offsets_and_lengths = self.offsets_and_lengths.reshape(1, 2)
+            starts = offsets_and_lengths[:, 0]
+            lengths = offsets_and_lengths[:, 1]
+            valid = starts != MAX_UINT_64
+            ends = starts + lengths
+            return starts, ends, valid
+
         # Localize coordinates via modulo (vectorized)
         shard_shape = np.array(self.offsets_and_lengths.shape[:-1], dtype=np.uint64)
         localized = chunk_coords_array.astype(np.uint64) % shard_shape
diff --git a/tests/test_codecs/test_sharding.py b/tests/test_codecs/test_sharding.py
index 233cc4cb77..2325069dd0 100644
--- a/tests/test_codecs/test_sharding.py
+++ b/tests/test_codecs/test_sharding.py
@@ -16,6 +16,7 @@
     ShardingCodecIndexLocation,
     TransposeCodec,
 )
+from zarr.codecs.sharding import MAX_UINT_64, _ShardIndex
 from zarr.core.buffer import NDArrayLike, default_buffer_prototype
 from zarr.storage import StorePath, ZipStore
 
@@ -554,3 +555,30 @@ def test_sharding_mixed_integer_list_indexing(store: Store) -> None:
     s3 = sharded[0:5, 1, 0:3]
     assert c3.shape == s3.shape == (5, 3)  # type: ignore[union-attr]
     np.testing.assert_array_equal(c3, s3)
+
+
+def test_sharding_zero_dimensional() -> None:
+    """Regression test for https://github.com/zarr-developers/zarr-python/issues/3751"""
+    arr = zarr.create_array({}, shape=(), dtype="f4", chunks=(), shards=())
+    arr[()] = 42.0
+    assert arr[()] == pytest.approx(42.0)
+    # Overwriting should also work
+    arr[()] = 43.0
+    assert arr[()] == pytest.approx(43.0)
+
+
+def test_shard_index_get_chunk_slices_vectorized_zero_dimensional() -> None:
+    """Directly cover the 0-D path in _ShardIndex.get_chunk_slices_vectorized."""
+    # For a 0D array offsets_and_lengths has shape (2,) — reshape to (1, 2) inside.
+    index = _ShardIndex(np.array([10, 4], dtype=np.uint64))
+    chunk_coords = np.empty((1, 0), dtype=np.uint64)
+    starts, ends, valid = index.get_chunk_slices_vectorized(chunk_coords)
+    np.testing.assert_array_equal(starts, np.array([10], dtype=np.uint64))
+    np.testing.assert_array_equal(ends, np.array([14], dtype=np.uint64))
+    np.testing.assert_array_equal(valid, np.array([True]))
+
+    # Empty/unwritten chunk case
+    index_empty = _ShardIndex(np.array([MAX_UINT_64, MAX_UINT_64], dtype=np.uint64))
+    starts_e, _ends_e, valid_e = index_empty.get_chunk_slices_vectorized(chunk_coords)
+    np.testing.assert_array_equal(starts_e, np.array([MAX_UINT_64], dtype=np.uint64))
+    np.testing.assert_array_equal(valid_e, np.array([False]))