Chinese media is reporting that the 32-year-old is in isolation at Jinan hospital, which specialises in infectious diseases.
Fellaini, who spent 11 seasons in England with United and Everton, recently returned to the country after a spell in Dubai following the outbreak of Covid-19.
“The official test confirmed that the player Fellaini has tested positive for the coronavirus during the quarantine observation period,” the club said in a statement.
“During this period, the player’s body temperature has been normal and there are no other discomforts. He has received further observation and treatment at a designated medical institution.”
Fellaini used a post on Twitter to express gratitude for the treatment he is receiving.
“Dear friends, I have been tested for coronavirus and my test result is positive,” Fellaini wrote.
“Thanks to the fans, medical staff and the club for their care and attention. I will follow the treatment and hope to return to the game as soon as possible. Please everyone stay safe.”