"I'm going to stand up and take it like a man, go on from there," he said Monday.
Griese was pulled over Saturday on an interstate outside Denver. Police said he was traveling 80 mph in a 65 mph zone.
He said at a news conference that he had a couple of drinks at dinner with a friend before heading home.
"I understand the seriousness of the charges and I'm going to take full responsibility for it because that's just the way that I am," he said.
Griese faces a Jan. 16 court date.
He failed roadside sobriety and breathalyzer tests and was taken to a detoxification facility in Aurora, Colorado State Patrol trooper Rob Marone said. Griese's blood-alcohol content was above the 0.10-percent legal limit, but Marone would not be more specific.
Griese was one of 130 people arrested Saturday in a law enforcement campaign to crack down on drunken driving. Officers set up checkpoints and randomly check drivers. Others targeted areas prone to drunken driving.
Griese was the NFL's highest-rated passer until injuring his right shoulder Sept. 17 against Oakland. He missed a game because of the injury and has said he might need surgery during the offseason to repair torn cartilage.
Griese, who helped lead Michigan to a national championship in 1997, threw for 3,032 yards and 14 touchdowns last season.
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