これを試してください：
SELECT `AUTO_INCREMENT` INTO @AutoInc
FROM INFORMATION_SCHEMA.TABLES
WHERE TABLE_SCHEMA = 'database_name' AND TABLE_NAME = 'another_table_name';
SET @s:=CONCAT('ALTER TABLE `database_name`.`table_name` AUTO_INCREMENT=', @AutoInc);
PREPARE stmt FROM @s;
EXECUTE stmt;
DEALLOCATE PREPARE stmt;