McDavid's positive test came during medical testing earlier on Monday.
"Since that time, he has been in voluntary self-quarantine at his home. He will continue to be monitored and will follow all associated health protocols," the franchise said in a statement.
The Oilers said that McDavid is "feeling well and is experiencing mild symptoms." He is quarantining near Toronto, where his offseason home is located.
McDavid, 23, has 469 points in 351 career games for the Oilers. He had 97 points in 64 games this season, finishing fifth in the most valuable player voting.
The diagnosis comes one week after the NHL completed its restarted season with the Stanley Cup Final in Edmonton, Alberta. Between the hub cities in Edmonton and Toronto, the league administered 33,394 COVID-19 tests among each playoff team's 52-member traveling staff, including players, and reported zero positive results.
The mandatory testing phase has concluded, according to the NHL.