Puljujarvi, 20, who hadn't played since Feb. 15 because of the injury, was the fourth overall pick in the 2016 draft.
He has four goals and nine points in 45 games this season, after notching 12 goals and 20 points in 65 games with the Oilers last season.
He has also spent time with Edmonton's AHL club in Bakersfield.
"This injury has been bothering Jesse for some time now and after careful consideration with Jesse, his agent and our medical staff, the best decision was to have the surgery and miss the remainder of the season," Oilers assistant general manager Keith Gretzky said in a release last week. "We expect Jesse to rehabilitate and train throughout the summer and be 100 percent ready to go for training camp in September."