The statement said the Alouettes "fully respect" Sam's decision and "rally around him to offer him all time and support needed."
The Alouettes said Sam "is welcome to come back whenever he feels ready."
The team said it would offer no further comment for the moment.
Sam, a defensive end, signed a two-year deal with the Alouettes last month.
He is the first openly gay player to be drafted by an National Football League team. The St. Louis Rams selected the pass rusher in the seventh round in 2014.
He appeared in four pre-season games before the team released him, then had a short stint on the Dallas Cowboys' practice squad that ended in October without his playing a regular-season down in the NFL.