Strict ASA championship play rules? I presume that you have no substitutes. If he has to leave the game, he is declared out and his spot becomes an automatic out in the lineup. If another person is injured and must leave the game, leaving you two down, then play cannot continue and you forfeit. There is no courtesy runner provision in adult slow pitch.
All of that said, your local league may have a provision for a courtesy runner or playing shorthanded without penalty when a player becomes injured. You'd have to check the local rules.