diff --git a/sqlglot/dialects/bigquery.py b/sqlglot/dialects/bigquery.py
index d8769ceb1c..a93c98ee16 100644
--- a/sqlglot/dialects/bigquery.py
+++ b/sqlglot/dialects/bigquery.py
@@ -203,8 +203,10 @@ def normalize_identifier(cls, expression: E) -> E:
             while isinstance(parent, exp.Dot):
                 parent = parent.parent
 
-            if not (isinstance(parent, exp.Table) and parent.db) and not expression.meta.get(
-                "is_table"
+            if (
+                not isinstance(parent, exp.UserDefinedFunction)
+                and not (isinstance(parent, exp.Table) and parent.db)
+                and not expression.meta.get("is_table")
             ):
                 expression.set("this", expression.this.lower())
 
diff --git a/tests/test_optimizer.py b/tests/test_optimizer.py
index 40eef9fe14..56b36eea03 100644
--- a/tests/test_optimizer.py
+++ b/tests/test_optimizer.py
@@ -229,6 +229,17 @@ def test_qualify_columns(self):
             'WITH "x" AS (SELECT "y"."a" AS "a" FROM "DB"."Y" AS "y" CROSS JOIN "a"."b"."INFORMATION_SCHEMA"."COLUMNS" AS "columns") SELECT "x"."a" AS "a" FROM "x"',
         )
 
+        self.assertEqual(
+            optimizer.qualify.qualify(
+                parse_one(
+                    "CREATE FUNCTION udfs.`myTest`(`x` FLOAT64) AS (1)",
+                    read="bigquery",
+                ),
+                dialect="bigquery",
+            ).sql(dialect="bigquery"),
+            "CREATE FUNCTION `udfs`.`myTest`(`x` FLOAT64) AS (1)",
+        )
+
         self.check_file("qualify_columns", qualify_columns, execute=True, schema=self.schema)
 
     def test_qualify_columns__with_invisible(self):