The news came from Arsenal manager Mikel Arteta, whose side are battling for honours on four fronts.
Saka suffered the injury in Arsenal's 5-1 win at Crystal Palace on Saturday.
Asked about the 23-year-old England international's condition, Arteta said: "It is not looking good. He will be out for many weeks."
England international Saka was filmed leaving Selhurst Park on crutches, souring what had been a comprehensive second win over the Eagles in four days after Gabriel Jesus' hat-trick secured Arsenal's passage to the Carabao Cup semi-finals.
Arsenal are also on course to progress to the Champions League knock-out stages and embark on their FA Cup campaign next month.
Arteta said: "I cannot be too specific because I don't know, but it will be many weeks.
"It's a huge blow. He's obviously a big player for us and you just have to see the impact that he has had on the team. But it's going to be a really good exercise for us to think of ways to overcome another challenge because we've had a lot over the season."
In a secondary blow to Arteta, the Spaniard also said he will be without Raheem Sterling, the obvious back-up option for Saka, for a lengthy period after the on-loan Chelsea winger suffered a knee injury prior to Arsenal's win at Palace.
Arteta insisted Saka, who has missed only seven league matches in the past three-and-a-half seasons, would be back before the conclusion of the campaign. But he admitted his player is struggling to come to terms with the setback.
"He (Saka) was gutted," continued Arteta. "You can tell that he has not been injured because he was really, really emotional and really down.
"And we need to lift him up. It is a big part of his job. He will be fine but he is going to need a few days.
"He will immediately realise that he is so important in that dressing room. His energy level, his body language, and how he communicates with the rest of the team has to be really good because it is the only way at the moment he can help, so he better do that well."
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