Tuesday's move comes two days after Johnson lost 10 yards on one of his two runs in Washington's 30-27 overtime loss to the Houston Texans.
The 30-year-old Johnson signed a three-year, incentive-laden contract with Washington in March.
He finished last season with the Cincinnati Bengals after being released by the Kansas City Chiefs in November. His time in Kansas City was marred by off-the-field problems, including two suspensions in his last 12 months with the team.
Johnson's best years were 2005-06, when he had consecutive 1,750-yard seasons. He has run for more than 6,000 yards in the NFL.