Milan's statement claims the club has "informed the relevant authorities and the player has been promptly placed in quarantine at home. All other team members and staff have tested negative."
The Serie A side conducted a round of tests ahead of Thursday's Europa League visit from Norwegian outfit FK Bodo/Glimt.
Milan defender Leo Duarte previously tested positive for the coronavirus on Wednesday, and like Ibrahimovic, has been forced to quarantine at home.
Ibrahimovic, 38, penned a one-year extension with Milan, and kicked off the 2020-21 campaign in style with both goals in the Rossoneri's 2-0 win over Bologna on Monday.