The diagnosis is especially hard for Towns, whose mother, Jacqueline Cruz-Towns, died at 59 on April 13 from complications of COVID-19. She had dealt with the virus for a month.
Towns said before the season that six other family members have also died from complications of the virus.
"Prior to tonight's game, I received yet another awful call that I tested positive for COVID," Towns said in a statement shared on social media. "I will immediately isolate and follow every protocol. I pray every day that this nightmare of a virus will subside and I beg everyone to continue to take it seriously by taking all the necessary precautions. ...
"It breaks my heart that my family, and particularly my father and sister continue to suffer from the anxiety that comes along with this diagnosis as we know all too well what the end result could be. To my niece and nephew ... I promise you I will not end up in a box next to grandma and I will beat this."
Gersson Rosas, the team's president of basketball operations, said during a news conference Friday that the organization has had two positive tests -- including Towns -- over the past two days and that one player is in the league's contact tracing protocols.
"It's heartbreaking," Rosas said of Towns' diagnosis. "It's a lesson for all of us. Basketball is a microcosm of society right now and you can do the right things -- our protocol has been strong. Our staff has done an unbelievable job of making sure we test, we mask, we follow protocol. But this virus is powerful and its creative.
"... Karl is the most important part of this organization," Rosas added. "What he's gone through, what Karl Sr. has gone through -- it couldn't be more heartbreaking."
Towns, 25, missed six games this season with a wrist injury but returned to the court last week. He's averaging 22 points, 12.5 rebounds and 4.3 assists in four games.
ESPN's Malika Andrews contributed to this report.