Griffin experienced knee discomfort during a workout Wednesday and, after undergoing tests in Los Angeles, was scratched from the roster.
The Los Angeles Clippers released a statement saying Griffin had been diagnosed with a medial meniscus tear in his left knee and would have arthroscopic surgery. He is expected to be ready for training camp later this year.
riffin originally injured the knee during a first-round playoff game against Memphis.
He was replaced on the Olympic roster by No. 1 NBA draft pick Anthony Davis, who had been among the last players trimmed from the squad.
Kevin Durant scored 24 points and grabbed 10 rebounds in Thursday's 113-59 exhibition win while Andre Iguodala had 18 points and hit 4-of-6 from 3-point range.
The Dominican Republic, coached by Kentucky's John Calapari, reached the final Olympic qualifying tournament in Venezuela earlier this month but was unable to earn a bid to the Games.
The Americans will play additional exhibition games against Brazil, Britain, Argentina and Spain leading up to the Olympics. All of those teams will be in London competing for the basketball gold medal.
Olympic basketball competition begins July 29, with the Americans meeting France in the first of their five round-robin group games. The top four teams in each of the two six-team groups will reach the quarterfinals.
The gold medal game will be played Aug. 12.