Anisimov, 29, got hurt in the first period of Thursday night's 5-2 loss at Vancouver. He has 13 goals and five assists in 36 games.
Anisimov joins Corey Crawford on Chicago's injured list. The Blackhawks put the goaltender on IR on Wednesday with an upper-body injury.
The Blackhawks activated defenseman Cody Franson before Friday night's game at Edmonton. Franson had one goal and six assists in 19 games when he was placed on IR on Dec. 13.