The move is retroactive to Tuesday, and Bryant won't be eligible to return until May 6 at Arizona.
Bryant, who signed a seven-year, $182 million free-agent deal in March, is still looking for his first home run with the Rockies. He's batting .281 with four RBIs and 12 strikeouts in 65 plate appearances.
An MRI Friday showed no structural issues.
Manager Bud Black said Bryant has been experiencing back soreness since a week ago in Detroit and believes it has affected his early performance.
"He would never tell you that, but I do think it has limited him," Black said.
The Rockies recalled infielder Elehuris Montero from Triple-A Albuquerque to replace Bryant. He was expected to arrive sometime during Friday's game against Cincinnati.
Sam Hilliard was to start in left field Friday night.