The 20-year-old defenseman will have surgery for a torn labrum and is expected to be sidelined 4-6 months. Drysdale was injured in a 4-0 loss to the Vegas Golden Knights on Friday.
The Ducks end the regular season against the Los Angeles Kings on April 13.
"For our team, that is a massive blow," Anaheim coach Dallas Eakins said. "That kid is a big part of our team, especially our back end. His last three or four games had really started to turn it up a notch. No. 1, it's devastating for our team, and that's where we're going to have to have other people step up and take those extra minutes. For Jamie, individually, this is going to be a young man we're going to have to keep a really close eye on.
"He's a hockey nerd; he loves to play, he loves to compete. He thinks about the game every day and now, to have to go through this process of not only getting things fixed but then going through the rehab, the restrengthening and then getting ready to play again, that can be mentally exhausting sometimes."
Selected by the Ducks in the first round (No. 6) of the 2020 NHL Draft, Drysdale did not have a point in eight games this season and averaged 17:37 of ice time. He has 40 points (seven goals, 33 assists) in 113 NHL games.
Anaheim ended a seven-game losing streak with a 4-3 win against the Toronto Maple Leafs at Honda Center on Sunday with 11 forwards and seven defensemen for the second consecutive game.
The Ducks visit the San Jose Sharks on Tuesday (10:30 p.m. ET; ESPN, SN NOW).
NHL.com independent correspondent Dan Arritt contributed to this report
