Lavery suffered the injury during Sunday's pre-season friendly against South Yorkshire neighbours Doncaster at the Keepmoat Stadium and the 21-year-old forward faces around two months on the sidelines.
"They call it like a car crash injury. We thought it might be ACL, but it's not. It's going to be a couple of months," Owls boss Stuart Gray said.
Gray also added that Lavery will see a specialist on Tuesday afternoon and that he hopes surgery will not be necessary.
Lavery spent time on loan with Plymouth last season, scoring three goals in eight appearances for the Sky Bet League Two club.
He has played 35 senior games so far in his fledgling career, including 10 starts for Wednesday.