The Rangers made the announcement 3½ hours before game time. Padilla was diagnosed with the illness last week and missed a start against Boston. The team thought he'd recovered and was ready to return to the rotation.
Doug Mathis, normally a long reliever, will pitch in place of Padilla.
Several members of the team were hit by the flu bug, no other cases of swine flu were confirmed. Most members of the ballclub most were feeling better after the team returned from Kansas City on Sunday.