diff --git a/json/tests/draft7/optional/format/hostname.json b/json/tests/draft7/optional/format/hostname.json
index a8ecd194..866a6178 100644
--- a/json/tests/draft7/optional/format/hostname.json
+++ b/json/tests/draft7/optional/format/hostname.json
@@ -112,6 +112,16 @@
                 "description": "single label ending with digit",
                 "data": "hostnam3",
                 "valid": true
+            },
+            {
+                "description": "empty string",
+                "data": "",
+                "valid": false
+            },
+            {
+                "description": "single dot",
+                "data": ".",
+                "valid": false
             }
         ]
     }
diff --git a/jsonschema/_format.py b/jsonschema/_format.py
index 789fe4f2..9b4e67b6 100644
--- a/jsonschema/_format.py
+++ b/jsonschema/_format.py
@@ -272,6 +272,10 @@ def is_ipv6(instance: object) -> bool:
         draft7="hostname",
         draft201909="hostname",
         draft202012="hostname",
+        # fqdn.FQDN("") raises a ValueError due to a bug
+        # however, it's not clear when or if that will be fixed, so catch it
+        # here for now
+        raises=ValueError,
     )
     def is_host_name(instance: object) -> bool:
         if not isinstance(instance, str):