The striker made the announcement on Twitter, writing that he tested negative on Wednesday but positive on Thursday, ahead of a Europa League match against Bodø/Glimt.
"No symptoms what so ever," the ever confident star said. "Covid had the courage to challenge me. Bad idea."
The club did not say when Ibrahimovic would return to play.
Both the US Centers for Disease Control and Prevention and the World Health Organization recommend asymptomatic people isolate for 10 days after testing positive.