Woodford was optioned to Triple-A Memphis on Monday.
Woodford struggled during the Cardinals' weekend series against the Pirates and allowed three runs on four hits and a walk while striking out one in two innings across two relief appearances. The right-hander will be stretched out with the Triple-A club and could be an option to rejoin the big-league club as a starter at some point, Derrick Goold of the St. Louis Post-Dispatch reports. Left-hander Brandon Waddell was recalled as part of a corresponding move.