diff --git a/src/datasets/load.py b/src/datasets/load.py
index 2dab9f7a7e6..dbd6abad46a 100644
--- a/src/datasets/load.py
+++ b/src/datasets/load.py
@@ -37,6 +37,7 @@
 import yaml
 from fsspec.core import url_to_fs
 from huggingface_hub import DatasetCard, DatasetCardData, HfApi, HfFileSystem
+from huggingface_hub.utils import GatedRepoError, RepositoryNotFoundError, RevisionNotFoundError
 
 from . import config
 from .arrow_dataset import Dataset
@@ -1836,28 +1837,26 @@ def dataset_module_factory(
                     token=download_config.token,
                     timeout=100.0,
                 )
-            except Exception as e:  # noqa catch any exception of hf_hub and consider that the dataset doesn't exist
-                if isinstance(
-                    e,
-                    (
-                        OfflineModeIsEnabled,
-                        requests.exceptions.ConnectTimeout,
-                        requests.exceptions.ConnectionError,
-                    ),
-                ):
-                    raise ConnectionError(f"Couldn't reach '{path}' on the Hub ({type(e).__name__})")
-                elif "404" in str(e):
-                    msg = f"Dataset '{path}' doesn't exist on the Hub or cannot be accessed"
-                    raise DatasetNotFoundError(msg + f" at revision '{revision}'" if revision else msg)
-                elif "401" in str(e):
-                    msg = f"Dataset '{path}' doesn't exist on the Hub or cannot be accessed"
-                    msg = msg + f" at revision '{revision}'" if revision else msg
-                    raise DatasetNotFoundError(
-                        msg
-                        + f". If the dataset is private or gated, make sure to log in with `huggingface-cli login` or visit the dataset page at https://huggingface.co/datasets/{path} to ask for access."
-                    )
-                else:
-                    raise e
+            except (
+                OfflineModeIsEnabled,
+                requests.exceptions.ConnectTimeout,
+                requests.exceptions.ConnectionError,
+            ) as e:
+                raise ConnectionError(f"Couldn't reach '{path}' on the Hub ({e.__class__.__name__})") from e
+            except GatedRepoError as e:
+                message = f"Dataset '{path}' is a gated dataset on the Hub."
+                if "401 Client Error" in str(e):
+                    message += " You must be authenticated to access it."
+                elif "403 Client Error" in str(e):
+                    message += f" Visit the dataset page at https://huggingface.co/datasets/{path} to ask for access."
+                raise DatasetNotFoundError(message) from e
+            except RevisionNotFoundError as e:
+                raise DatasetNotFoundError(
+                    f"Revision '{revision}' doesn't exist for dataset '{path}' on the Hub."
+                ) from e
+            except RepositoryNotFoundError as e:
+                raise DatasetNotFoundError(f"Dataset '{path}' doesn't exist on the Hub or cannot be accessed.") from e
+
             if filename in [sibling.rfilename for sibling in dataset_info.siblings]:  # contains a dataset script
                 fs = HfFileSystem(endpoint=config.HF_ENDPOINT, token=download_config.token)
                 if _require_custom_configs or (revision and revision != "main"):
diff --git a/tests/test_load.py b/tests/test_load.py
index 2c02e834892..3547a0c00a0 100644
--- a/tests/test_load.py
+++ b/tests/test_load.py
@@ -1067,13 +1067,9 @@ def test_load_dataset_from_hub(self):
             str(context.exception),
         )
         with self.assertRaises(DatasetNotFoundError) as context:
-            datasets.load_dataset("_dummy", revision="0.0.0")
+            datasets.load_dataset("HuggingFaceFW/fineweb-edu", revision="0.0.0")
         self.assertIn(
-            "Dataset '_dummy' doesn't exist on the Hub",
-            str(context.exception),
-        )
-        self.assertIn(
-            "at revision '0.0.0'",
+            "Revision '0.0.0' doesn't exist for dataset 'HuggingFaceFW/fineweb-edu' on the Hub.",
             str(context.exception),
         )
         for offline_simulation_mode in list(OfflineSimulationMode):