Chychrun, 19, was injured during offseason training and is expected to make a full recovery.
"Confident I will come back from this better than ever," Chychrun wrote on Twitter. "Already looking forward to rejoining the guys."
Selected with the No. 16 pick in the 2016 NHL Draft, Chychrun had 20 points (seven goals, 13 assists) in 68 games last season.