The moves are expected to make room for injured forwards Marian Hossa and Patrick Sharp. Both sat out Monday's game against the Nashville Predators, but Blackhawks coach Joel Quenneville said they would be revaluated on Wednesday and could play Thursday against the St. Louis Blues.
Morin, who was recalled on Saturday, scored a goal against the Detroit Red Wings on Sunday.
Hayes had one goal and two goals in nine games with the Blackhawks. He had been with the Blackhawks since March 12.