Podría usar SQL dinámico para hacerlo, dentro de un procedimiento almacenado. Se vería así (no probado):
CREATE PROCEDURE drop_like (IN pattern VARCHAR(64))
BEGIN
DECLARE q tinytext;
DECLARE done INT DEFAULT FALSE;
DECLARE cur CURSOR FOR
SELECT CONCAT('DROP TABLE "', table_schema, '"."', table_name, '"')
FROM information_schema.tables WHERE table_type = 'BASE TABLE' AND table_name LIKE pattern;
DECLARE CONTINUE HANDLER FOR NOT FOUND SET done = TRUE;
OPEN cur;
drop_loop: LOOP
FETCH cur INTO q;
IF done THEN
LEAVE drop_loop;
END IF;
PREPARE stmt FROM @q;
EXECUTE stmt;
DEALLOCATE PREPARE stmt;
END LOOP;
CLOSE cur;
END;