Flacco told the team of a disc issue in his back last week just before the first full-team meeting. He is expected to miss at least a week.
The quarterback shuffle move will not preclude the Ravens from signing another experienced quarterback, including Colin Kaepernick.
Ravens owner Steve Bisciotti said Sunday the team was still considering Kaepernick, who became a flashpoint for debate last season when he kneeled during the national anthem to bring attention to civil rights issues.
"We're very sensitive to it, and we're monitoring it and we're still, as (general manager Ozzie Newsome) says, we're scrimmaging it," Bisciotti said at a fan forum with NFL commissioner Roger Goodell at M&T Bank Stadium. "We're trying to figure what's the right tact. Pray for us."
Woodrum, 24, signed with the New York Giants as an undrafted free agent last year following his college career at Liberty. He was cut by the Giants after rookie minicamp and later spent time with the Indianapolis Colts, Chicago Bears and the Buffalo Bills. He was released by the Bills on May 24.
Olson played at Stanford and transferred to Clemson for his senior season. He most recently played for the KC Phantoms of Champions Indoor Football.
The Ravens also said receiver/punt returner Michael Campanaro passed his physical and will be activated off the physically unable to perform list after missing the first four days of training camp with a toe injury.