The Swiss forward was hurt when he was hit in the face by a puck in Vancouver’s 4-2 loss at Calgary on Saturday.
The Canucks said on Twitter that Baertschi will not need to have surgery.
Baertschi has eight goals and 10 assists in 30 games this season.
He is the second Canucks forward to suffer a long-term injury in the past week. Bo Horvat suffered a fractured foot in Vancouver’s 3-0 win over Carolina on Tuesday and will miss up to six weeks.
Horvat and Baertschi had recently been part of a potent scoring line with impressive rookie Brock Boeser.