The Canadiens also announced they had waived defenseman Karl Alzner.
Weise, a former Canadien, has played 42 games in 2018-19 with five goals and six assists. The 30-year-old had 59 points in 152 games with Montreal from 2013-2016.
Weise has 54 goals and 66 assists in 481 career NHL regular-season games since his debut in 2010-11. He also has played for the New York Rangers, Vancouver and Chicago.
Folin, a 27-year-old Swede, has been in 26 games with Philadelphia this season, recording two assists.
Folin has seven goals, 31 assists and 96 penalty minutes in 209 career NHL regular-season games with Minnesota, Los Angeles and Philadelphia since his debut in 2013-14.
Schlemko, acquired in a trade with Vegas in 2017, had two assists in 18 games with the Canadiens this season.
Froese signed as a free agent with Montreal in 2017. He was leading the American Hockey League's Laval Rocket with 14 goals.