The midfielder made his first start since last December in Wednesday's EFL Cup third-round clash at West Bromwich Albion.
Gundogan, who was previously sidelined with a serious injury to his right knee, limped off after an hour of the game at The Hawthorns, which finished 2-1 to the visitors.
Man City's medical department ran tests on the Germany international's knock, which affected his left knee, and have announced that it is a sprain.
A report on the club's website read: "It is too early at this stage to give an exact timeframe on his absence but he is expected to be back on the training field in the coming days."
Gundogan, meanwhile, tweeted: "Hi all, thank you for all your messages! I'm happy to tell you my injury is nothing serious and I hope to be back soon on the pitch!"
The player cost Man City a reported fee of £20m to sign from Borussia Dortmund in 2016, becoming Pep Guardiola's first signing at the club.