The five-time All-Star was injured in the third quarter. Love scored six points and had seven rebounds in 24 minutes for Cleveland, which blew a late lead before winning 132-122 in double overtime.
The Cavaliers said X-rays taken Saturday confirmed the fracture. Love is listed as doubtful for Sunday's home game against the Miami Heat, and it's likely the 34-year-old could miss several games to give the thumb time to heal.
Love's injury is the latest for the Cavaliers, who have had their share early this season. All-Star guard Darius Garland missed six games with a left eye injury, forward Dean Wade is currently sidelined with a knee infection, and All-Star guard Donovan Mitchell has been slowed by a sprained ankle.
Center Jarrett Allen returned Friday after missing two games with an illness.
Love is in his ninth season with Cleveland after spending his first six NBA seasons in Minnesota. He has been coming off the bench the past two seasons for the Cavaliers, who snapped a five-game losing streak with their win over the Hornets. Love is averaging 11.3 points and 7.4 rebounds in 21.3 minutes per game.