The Rangers made the announcement 3½ hours before gametime. 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, but Padilla told club officials on Monday night that he needed more time.
Doug Mathis, normally a long reliever, took Padilla's place. Mathis made his second start of the season and sixth of his career.
Padilla, who hasn't started since July 17 after coming down with the flu, threw in the bullpen prior to Tuesday night's game.
Rangers manager Ron Washington said Padilla is a possibility to start Thursday night against Seattle.
"We'll give him another day," Washington said. "He said his legs didn't feel good enough that he thought he could go out there. ... If Padilla is ready to go Thursday, he'll go Thursday."
Rookie Derek Holland is still scheduled to start for Texas on Thursday night, with Kevin Millwood set for Friday night. But Millwood is recovering from a strained left gluteus muscle which forced him out of his last start after two innings on Sunday.
Millwood had a throwing session Tuesday and said he felt better. But the club is unsure if Millwood will be healthy enough to start on Friday night.