The news was announced by the Serie A club in a short statement ahead of their Europa League game against Bodo/Glimt and Ibrahimovic posted on Twitter: "I tested negative to Covid yesterday and positive today. No symptoms whatsoever. COVID had the courage to challenge me. Bad idea."
Milan said they have "informed the relevant authorities and the player has been promptly placed in quarantine at home. All other team members and staff have tested negative."
Ibrahimovic's Milan teammate Leo Duarte tested positive for the coronavirus on Wednesday.
Ibrahimovic, 38, signed a one-year contract extension with Milan last month that will see him remain at the club for the 2020-21 campaign. He got the season off to a winning start against Bologna on Monday, scoring both goals in a 2-0 win.
Milan extended their unbeaten run to 15 games in all competitions as they picked up where they left off last season, suggesting they are capable of battling for a Champions League spot.
Ibrahimovic returned to Milan last December after leaving MLS side LA Galaxy.
"Italy has always given me so much and, in this dramatic moment, I want to give back even more to this country that I love," he said in a video message to launch the fundraiser.
"I count on the generosity of my colleagues, of all professional athletes and of those who want to make a small or large donation according to their possibilities, to kick this virus away."