Gagner suffered the injury in Edmonton's 5-2 exhibition win over Vancouver on Saturday.
Gagner collided on the side boards with Vancouver's Zack Kassian, and Kassian's stick knocked out some of Gagner's teeth.
Kassian received a four-minute penalty on the play.
The team said Gagner is out indefinitely.
The 24-year-old Gagner had 14 goals and 38 points in 48 games with the Oilers last season. He has 91 goals and 167 assists in 414 games over six seasons with Edmonton.