Padilla was scheduled to start Monday night for the Rangers against the Cleveland Indians. Washington said rookie Doug Mathis will be moved up a day in the rotation to replace Padilla.
Washington said he was hopeful Padilla would be back to start Tuesday night against Cleveland.
If Padilla is away from the team for an extended period, Washington said left-hander A.J. Murray would be recalled from Triple-A Oklahoma to make Tuesday night's start. The Rangers probably would not have to open a roster spot for Murray because they would be given bereavement leave for Padilla, which would last from three to seven days.
Padilla has been the Rangers' top starter with a 7-2 record and 3.67 ERA.