Shooting guard Marcus Smart confirmed shortly after the team's announcement that he was the player in question.
"I'm OK. I feel fine. I don't feel any of the symptoms, but I can't stress enough practicing social distancing and really keeping yourself away from a large group of people," Smart said.
The Celtics are awaiting further test results and said they will make additional announcements when appropriate.
Smart becomes the fifth known player to test positive, joining Rudy Gobert and Donovan Mitchell of the Utah Jazz as well as Brooklyn Nets star Kevin Durant. Detroit Pistons forward Christian Wood reportedly also tested positive for COVID-19.
Five unidentified players have also contracted the COVID-19 virus - two from the Los Angeles Lakers and three more who play for the Nets. Three members of the Philadelphia 76ers organization and one individual employed by the Denver Nuggets also tested positive, bringing the total number of cases within the NBA to 14.