Towns' diagnosis comes nine months after his mother, Jacqueline, died at 59 from complications of the virus. She battled the coronavirus for a month.
Towns said before the season started that six other family members have died from COVID-19 complications.
"Prior to tonight's game, I received yet another awful call that I tested positive for COVID," Towns said in a statement Friday. "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."
Timberwolves president of basketball operations Gersson Rosas told reporters the franchise has recorded two positive tests, including Towns, over the last two days. He noted that one player is in the NBA's contact tracing protocols.
"It's heartbreaking," Rosas said of Towns' COVID-19 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 it's creative.
"... Karl is the most important part of this organization. What he's gone through, what Karl Sr. has gone through -- it couldn't be more heartbreaking."
The 25-year-old Towns has missed six games this season due to a wrist injury, but he returned to the lineup last week. He has averaged 22 points, 12.5 rebounds and 4.3 assists in four games.
Also Friday, the Washington Wizards announced that six additional players have tested positive for COVID-19, making it a total of nine Wizards players who are in the league's health and safety protocols.
As a result, the Wizards had their next two games against the Cleveland Cavaliers -- initially scheduled for Sunday and Monday -- postponed. Washington has had four consecutive games pushed back since it last played Monday against the Phoenix Suns.