diff --git a/src/parser/mod.rs b/src/parser/mod.rs
index 6f81e1e4e..4d642919e 100644
--- a/src/parser/mod.rs
+++ b/src/parser/mod.rs
@@ -3941,9 +3941,15 @@ impl<'a> Parser<'a> {
         match next_token.token {
             Token::Word(w) if w.keyword == Keyword::PRIMARY || w.keyword == Keyword::UNIQUE => {
                 let is_primary = w.keyword == Keyword::PRIMARY;
-                if is_primary {
-                    self.expect_keyword(Keyword::KEY)?;
-                }
+
+                // parse optional [KEY]
+                let _ = self.parse_keyword(Keyword::KEY);
+
+                // optional constraint name
+                let name = self
+                    .maybe_parse(|parser| parser.parse_identifier())
+                    .or(name);
+
                 let columns = self.parse_parenthesized_column_list(Mandatory, false)?;
                 Ok(Some(TableConstraint::Unique {
                     name,
diff --git a/tests/sqlparser_mysql.rs b/tests/sqlparser_mysql.rs
index 00901799f..5aeffb0b6 100644
--- a/tests/sqlparser_mysql.rs
+++ b/tests/sqlparser_mysql.rs
@@ -297,6 +297,62 @@ fn parse_create_table_auto_increment() {
     }
 }
 
+#[test]
+fn parse_create_table_unique_key() {
+    let sql = "CREATE TABLE foo (id INT PRIMARY KEY AUTO_INCREMENT, bar INT NOT NULL, UNIQUE KEY bar_key (bar))";
+    let canonical = "CREATE TABLE foo (id INT PRIMARY KEY AUTO_INCREMENT, bar INT NOT NULL, CONSTRAINT bar_key UNIQUE (bar))";
+    match mysql().one_statement_parses_to(sql, canonical) {
+        Statement::CreateTable {
+            name,
+            columns,
+            constraints,
+            ..
+        } => {
+            assert_eq!(name.to_string(), "foo");
+            assert_eq!(
+                vec![TableConstraint::Unique {
+                    name: Some(Ident::new("bar_key")),
+                    columns: vec![Ident::new("bar")],
+                    is_primary: false
+                }],
+                constraints
+            );
+            assert_eq!(
+                vec![
+                    ColumnDef {
+                        name: Ident::new("id"),
+                        data_type: DataType::Int(None),
+                        collation: None,
+                        options: vec![
+                            ColumnOptionDef {
+                                name: None,
+                                option: ColumnOption::Unique { is_primary: true },
+                            },
+                            ColumnOptionDef {
+                                name: None,
+                                option: ColumnOption::DialectSpecific(vec![Token::make_keyword(
+                                    "AUTO_INCREMENT"
+                                )]),
+                            },
+                        ],
+                    },
+                    ColumnDef {
+                        name: Ident::new("bar"),
+                        data_type: DataType::Int(None),
+                        collation: None,
+                        options: vec![ColumnOptionDef {
+                            name: None,
+                            option: ColumnOption::NotNull,
+                        },],
+                    },
+                ],
+                columns
+            );
+        }
+        _ => unreachable!(),
+    }
+}
+
 #[test]
 fn parse_create_table_comment() {
     let canonical = "CREATE TABLE foo (bar INT) COMMENT 'baz'";