diff --git a/swh/loader/git/dumb.py b/swh/loader/git/dumb.py
--- a/swh/loader/git/dumb.py
+++ b/swh/loader/git/dumb.py
@@ -77,7 +77,7 @@
         self.base_repo = base_repo
         self.objects: Dict[bytes, Set[bytes]] = defaultdict(set)
         self.refs = self._get_refs()
-        self.head = self._get_head()
+        self.head = self._get_head() if self.refs else {}
         self.packs = self._get_packs()
 
     def fetch_object_ids(self) -> None:
diff --git a/swh/loader/git/tests/test_loader.py b/swh/loader/git/tests/test_loader.py
--- a/swh/loader/git/tests/test_loader.py
+++ b/swh/loader/git/tests/test_loader.py
@@ -14,6 +14,7 @@
 import dulwich.repo
 import pytest
 
+from swh.loader.git import dumb
 from swh.loader.git.loader import GitLoader
 from swh.loader.git.tests.test_from_disk import FullGitLoaderTests
 from swh.loader.tests import (
@@ -257,6 +258,29 @@
             "snapshot": 1,
         }
 
+    def test_load_empty_repository(self, mocker):
+        class GitObjectsFetcherNoRefs(dumb.GitObjectsFetcher):
+            def _get_refs(self):
+                return {}
+
+        mocker.patch.object(dumb, "GitObjectsFetcher", GitObjectsFetcherNoRefs)
+
+        res = self.loader.load()
+
+        assert res == {"status": "uneventful"}
+
+        stats = get_stats(self.loader.storage)
+        assert stats == {
+            "content": 0,
+            "directory": 0,
+            "origin": 1,
+            "origin_visit": 1,
+            "release": 0,
+            "revision": 0,
+            "skipped_content": 0,
+            "snapshot": 1,
+        }
+
 
 class TestDumbGitLoaderWithPack(DumbGitLoaderTestBase):
     @classmethod