You can create recursive procedures following the same guidelines. First create the procedure with a simple body that throws an exception. You need to specify the SPECIFIC name of the procedure:

CREATE PROCEDURE updateFolderTotals(IN p_id VARCHAR(32), IN p_size BIGINT, IN p_files   INT, IN p_folders INT) 
  SPECIFIC updateFolderTotals_1 MODIFIES SQL DATA 
  SIGNAL SQLSTATE '45000'

Then alter the created procedure with the full body:

ALTER SPECIFIC ROUTINE updateFolderTotals_1
  BEGIN ATOMIC  
  DECLARE l_parentid VARCHAR(32); 
  UPDATE folders  
  SET tot_files = tot_files + p_files, 
    tot_size = tot_size + p_size , 
    tot_folders = tot_folders + p_folders 
  WHERE id = p_id;  

  SELECT parentid INTO l_parentid FROM folders WHERE id = p_id; 

  IF (l_parentid IS NOT NULL) THEN 
    CALL updateFolderTotals(l_parentid,p_size,p_files,p_folders); 
  END IF; 
END;