The 23-year-old, who is still recovering from surgery after suffering a smashed cheekbone against Inter Milan in late November, was tested before travelling to Italy for a check-up on Friday.
Osimhen also tested positive for Covid last January after returning from Christmas holidays in Nigeria.
"Victor Osimhen has tested positive for Covid-19 but is asymptomatic," Serie A team Napoli said in a statement, without specifying where the player currently is.
"Consequently, the local authorities have ordered that Osimhen self-isolate and the check-up will be rescheduled after he has tested negative and his period of isolation ends."
Osimhen had been training for Napoli while wearing a protective facemask and awaiting the go-ahead to return to action earlier than expected, after initially being ruled out for three months.
He had looked certain to miss the Cup of Nations, which kicks off in Cameroon on January 9, but was called up to the national squad.