The injury occurred during Edmonton's 3-2 win at Tampa Bay on Tuesday night.
Kane, 31, got tangled with Lightning defenseman Philippe Myers just inside the Edmonton defensive zone and while on the ice was cut by Tampa Bay forward Pat Maroon's skate blade 3 minutes, 27 seconds into the second period.
Kane was transported to a hospital and underwent a procedure Tuesday night. The team placed him on long-term injured reserve Wednesday.
Kane, who signed a four-year, $20.5 million contract with the Oilers in the offseason, has five goals and eight assists over 13 games this season.
"Thank you all for the kind wishes and prayers from over the past several hours," Kane said Wednesday in a statement. "Obviously last night was an extremely scary moment for me and I'm still in a little bit of shock.
"I would like to thank the entire training staff of the Edmonton Oilers and Tampa Bay Lightning, along with the all the doctors and paramedics who rushed to help treat and repair my injury. Without all of you, I know things would've been much worse and I'm sincerely grateful."
The Oilers said forwards Mattias Janmark and Klim Kostin have been recalled from the AHL's Bakersfield Condors.