Simons was injured on Saturday during Tottenham's 1-0 win at Wolverhampton Wanderers and left the pitch on a stretcher in the 63rd minute.
"Xavi will undergo surgery in the coming weeks and, following that, will then begin his rehabilitation with our medical team," the club said.
Netherlands midfielder Simons said on Sunday his season had "come to an abrupt end" after suffering a serious injury that is set to rule him out of the World Cup.
"They say life can be cruel and today it feels that way," the 23-year-old said in an Instagram post.
"My season has come to an abrupt end and I’m just trying to process it. Honestly, I’m heartbroken... All I’ve wanted to do is fight for my team and now the ability to do that has been snatched away from me… along with the World Cup. Representing my country this summer…just gone."
Simons was expected to be a key figure in Ronald Koeman's Netherlands squad for what would have been his second World Cup after his debut in 2022. He has earned 34 caps, most recently featuring in friendlies in March.
The injury is also a major blow for Tottenham during a difficult Premier League season, as the North London team sit 18th on 34 points, two points away from safety.