He is likely to be ruled out for several months.
"It's so so difficult for him, it's sad for him," manager Pep Guardiola told a news conference.
"We're going to miss him a lot, it's unlucky, but that's football. Now we need him to feel we are there and wait and come back safe. He’s going to be operated (on) and be back as soon as possible."
Gundogan joined City from Borussia Dortmund in June and was just settling into the side when he sustained the injury during Wednesday's 2-0 win over Watford.
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He had previously dislocated a kneecap with Dortmund, which delayed his City debut until mid-September.
Four other senior players - Sergio Aguero, Fernandinho (both suspended), Vincent Kompany and Fabian Delph (injured) - will also be missing on Sunday, when fourth-placed City host Arsenal, who are one place and one point ahead of them.
"Arsenal have huge quality and always buying the right players," Guardiola said.
"They have fast players, they can defend well, they can use the counter.
"We will have to be good to beat them."
Yaya Toure, left out earlier in the season because of fitness concerns and a falling-out with Guardiola, is expected to continue in midfield.
"You know the reason why he was out in the first part of the season," he said.
"Now he is playing like he can be, like I met him at Barcelona. There is no doubt about his quality."
(Reporting by Steve Tongue, editing by Ed Osmond)
