The 21-year-old has been sidelined since last November after dislocating his shoulder while representing Nigeria in the Africa Cup of Nations.
He has scored two goals in six league appearances, but has not played since November 8 because of his shoulder injury.
“Napoli can confirm that Victor Osimhen has tested positive for COVID-19 following his return to Italy,” Napoli said in a statement.
“Osimhen is currently asymptomatic and has not come into contact with the rest of the squad.”
The Italian side paid French club Lille a club record fee of up to 80 million euros ($94.6 million) to bring the forward to southern Italy on a five-year deal last summer. They are currently fifth in Serie A and travel to Cagliari on Sunday as the Italian league returns after the Christmas break.