diff --git a/fsspec/implementations/dirfs.py b/fsspec/implementations/dirfs.py
index 04f7479ad..b8119197d 100644
--- a/fsspec/implementations/dirfs.py
+++ b/fsspec/implementations/dirfs.py
@@ -66,7 +66,12 @@ def _relpath(self, path):
                 return path
             if path == self.path:
                 return ""
+            # S3FileSystem returns paths that do not start with a '/', so we
+            # need to remove the leading '/' from self.path if there is one there
+            # but not on the incoming path
             prefix = self.path + self.fs.sep
+            if not path.startswith(self.fs.sep) and self.path.startswith(self.fs.sep):
+                prefix = prefix[1:]
             assert path.startswith(prefix)
             return path[len(prefix) :]
         return [self._relpath(_path) for _path in path]
diff --git a/fsspec/implementations/tests/test_dirfs.py b/fsspec/implementations/tests/test_dirfs.py
index c04ba66a7..b4a0164c6 100644
--- a/fsspec/implementations/tests/test_dirfs.py
+++ b/fsspec/implementations/tests/test_dirfs.py
@@ -90,6 +90,18 @@ def test_path(fs, root, rel, full):
     assert dirfs._relpath(full) == rel
 
 
+@pytest.mark.parametrize(
+    "root, rel, full",
+    [
+        ("/root", "foo", "root/foo"),
+        ("/root", "foo", "/root/foo"),
+    ],
+)
+def test_path_no_leading_slash(fs, root, rel, full):
+    dirfs = DirFileSystem(root, fs)
+    assert dirfs._relpath(full) == rel
+
+
 def test_sep(mocker, dirfs):
     sep = mocker.Mock()
     dirfs.fs.sep = sep