The Rossoneri reached the next stage of qualifying for the Europa League last midweek after easily defeating Shamrock Rovers.
They followed that up with their opening Serie A match of the season on Monday versus Bologna.
In that game, they won 2-0 after Ibrahimovic scored a double.
Head coach Stefano Pioli now faces a selection headache for their fixture against Bodo/Glimt as the Swedish striker will now need to self-isolate.
Milan (@acMilan) September 24, 2020
"Zlatan Ibrahimovic has tested positive for Covid-19 following a second round of swab tests ahead of tonight's game against Bodø/Glimt," a club statement read.
"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."
Not only will he miss the Europa League, but he will be in the middle of quarantine during Milan's match against Crotone this weekend.
Within Italian regulations, he should be allowed back for the match against Spezia if fit.