The man, who was not identified and did not have symptoms of the illness, left the Santa Marta residence and went into isolation along with others with whom he had had direct contact, a statement said.
Someone else living in the residence – which has about 130 rooms and suites – tested positive for coronavirus when the pandemic hit Italy in March.
Pope Francis, who had part of one lung removed during an illness when he was a young man in his native Argentina, is tested regularly for Covid-19.
He had a normal schedule on Saturday, receiving three people in separate private audiences and addressing a large group of Italian police.
The Vatican, a tiny city-state surrounded by Rome, has been only lightly affected by the coronavirus, with about two dozen confirmed cases in total.
Three Vatican residents who tested positive recently have recovered, Saturday's statement added.
Four members of the Swiss Guard, the elite and colourfully dressed corps that protects the pope, tested positive for Covid-19 last week. – Reuters