In a news conference, Owens, a Republican, cited family reasons and a need to complete his second and last term as governor.
"It comes down to what you know in your heart is the right thing to do," he said. "The time is not right for me, for my family or for Colorado to make the kind of personal and professional commitment I know I must make to ensure victory."
Owens said he had the support of his family regardless of what decision he had made. He and his wife have been separated since September, according to KUSA-TV in Denver.
Owens was seen by many political observers as the strongest Republican candidate for Campbell's seat.
Several Democrats are already running for the Senate nomination, including millionaire businessman Rutt Bridges. More Democrats are considering the race.