diff --git a/neo4j/io/_bolt4.py b/neo4j/io/_bolt4.py
index 4968332c3..2d6c74064 100644
--- a/neo4j/io/_bolt4.py
+++ b/neo4j/io/_bolt4.py
@@ -164,7 +164,10 @@ def route(self, database):
 
         def fail(md):
             from neo4j._exceptions import BoltRoutingError
-            if md.get("code") == "Neo.ClientError.Procedure.ProcedureNotFound":
+            code = md.get("code")
+            if code == "Neo.ClientError.Database.DatabaseNotFound":
+                return  # surface this error to the user
+            elif code == "Neo.ClientError.Procedure.ProcedureNotFound":
                 raise BoltRoutingError("Server does not support routing", self.unresolved_address)
             else:
                 raise BoltRoutingError("Routing support broken on server", self.unresolved_address)
@@ -512,7 +515,10 @@ def route(self, database):
 
         def fail(md):
             from neo4j._exceptions import BoltRoutingError
-            if md.get("code") == "Neo.ClientError.Procedure.ProcedureNotFound":
+            code = md.get("code")
+            if code == "Neo.ClientError.Database.DatabaseNotFound":
+                return  # surface this error to the user
+            elif code == "Neo.ClientError.Procedure.ProcedureNotFound":
                 raise BoltRoutingError("Server does not support routing", self.unresolved_address)
             else:
                 raise BoltRoutingError("Routing support broken on server", self.unresolved_address)
diff --git a/tests/integration/test_neo4j_driver.py b/tests/integration/test_neo4j_driver.py
index 7de0b471b..4be1a2e15 100644
--- a/tests/integration/test_neo4j_driver.py
+++ b/tests/integration/test_neo4j_driver.py
@@ -81,7 +81,8 @@ def test_test_multi_db_specify_database(neo4j_uri, auth, target):
         assert "Database name parameter for selecting database is not supported in Bolt Protocol Version(3, 0)." in error.args[0]
     except ClientError as error:
         # FAILURE {'code': 'Neo.ClientError.Database.DatabaseNotFound' - This message is sent from the server
-        assert error.args[0] == "Unable to get a routing table for database 'test_database' because this database does not exist"
+        assert error.code == "Neo.ClientError.Database.DatabaseNotFound"
+        assert "test_database" in error.message
 
 
 def test_neo4j_multi_database_support_create(neo4j_uri, auth, target, requires_bolt_4x):