The 38-year-old former Sweden international will now have to undergo a period of self-isolation and must return a negative test before returning to action.
Ibrahimovic has made an electrifying start to the new season, scoring against Shamrock Rovers in the Europa League last week and netting a brace as AC Milan opened their Serie A campaign with a 2-0 win over Bologna on Monday.
The former Manchester United, Juventus and Paris Saint Germain striker will miss out when AC Milan meet Norwegian side Bodo/Glimt in the Europa League third qualifying round later on Thursday.
A statement from the Serie A club on their official website read: “Zlatan Ibrahimovic has tested positive for Covid-19 following a second round of swab tests ahead of tonight's game against Bodø/Glimt.
“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.”
Ibrahimovic rejoined AC Milan for a second stint in January after leaving Major League Soccer side LA Galaxy and scored 10 goals in 18 Serie A games last season.
He has recently signed a one-year contract extension at the San Siro which will expire after the 2020/2021 season.
