diff --git a/src/zarr/api/asynchronous.py b/src/zarr/api/asynchronous.py
index 6164cda957..adb4acffde 100644
--- a/src/zarr/api/asynchronous.py
+++ b/src/zarr/api/asynchronous.py
@@ -877,7 +877,10 @@ async def open_group(
             overwrite=overwrite,
             attributes=attributes,
         )
-    msg = f"No group found in store {store!r} at path {store_path.path!r}"
+    if zarr_format is not None:
+        msg = f"No Zarr {zarr_format} group found in store {store!r} at path {store_path.path!r}"
+    else:
+        msg = f"No Zarr group found in store {store!r} at path {store_path.path!r}"
     raise GroupNotFoundError(msg)
 
 
@@ -1290,7 +1293,10 @@ async def open_array(
                 overwrite=overwrite,
                 **kwargs,
             )
-        msg = f"No array found in store {store_path.store} at path {store_path.path}"
+        if zarr_format is not None:
+            msg = f"No Zarr {zarr_format} array found in store {store_path.store} at path {store_path.path}"
+        else:
+            msg = f"No Zarr array found in store {store_path.store} at path {store_path.path}"
         raise ArrayNotFoundError(msg) from err
 
 
diff --git a/tests/test_api.py b/tests/test_api.py
index adea150ae1..e1ef3864ab 100644
--- a/tests/test_api.py
+++ b/tests/test_api.py
@@ -45,6 +45,7 @@
 from zarr.core.buffer import NDArrayLike
 from zarr.errors import (
     ArrayNotFoundError,
+    GroupNotFoundError,
     MetadataValidationError,
     ZarrDeprecationWarning,
     ZarrUserWarning,
@@ -1547,3 +1548,33 @@ def test_unimplemented_kwarg_warnings(kwarg_name: str) -> None:
     kwargs = {kwarg_name: 1}
     with pytest.warns(RuntimeWarning, match=".* is not yet implemented"):
         zarr.create(shape=(1,), **kwargs)  # type: ignore[arg-type]
+
+
+def test_specific_fmt_error_message_group() -> None:
+    store = zarr.storage.MemoryStore()
+    # Create a group
+    zarr.create_group(store=store, path="my_group", zarr_format=3)
+    # Check that the new group exists
+    zarr.open_group(store=store, path="my_group", mode="r", zarr_format=3)
+    # Check error message when opening with wrong Zarr format
+    with pytest.raises(GroupNotFoundError, match="No Zarr 2 group found"):
+        zarr.open_group(store=store, path="my_group", mode="r", zarr_format=2)
+
+
+def test_specific_fmt_error_message_array() -> None:
+    store = zarr.storage.MemoryStore()
+    # Create an array
+    zarr.create_array(
+        store=store,
+        zarr_format=3,
+        data=np.array(
+            [
+                1,
+            ]
+        ),
+    )
+    # Check that the new array exists
+    zarr.open_array(store=store, mode="r", zarr_format=3)
+    # Check error message when opening with wrong Zarr format
+    with pytest.raises(ArrayNotFoundError, match="No Zarr 2 array found"):
+        zarr.open_array(store=store, mode="r", zarr_format=2)