Dustin Nippert will start in Padilla's place.
There are seven players who are feeling sick, including Frank Francisco, who is on the disabled list with walking pneumonia. Also down to some degree are Padilla, Eddie Guardado, Omar Vizquel, David Murphy, Kevin Millwood and Willie Eyre.
Padilla started coming down with symptoms on Tuesday night and felt progressively worse on Wednesday. Guardado was not at the ballpark on Wednesday and was the only other player not available for the game. Murphy was in the lineup, and Vizquel was available off the bench.
"They're doing everything to take care of everything, everybody," Rangers manager Ron Washington said of his training staff. "It is concerning, but the guys that have it deep aren't at the ballpark."
The Rangers had a team meeting on Wednesday afternoon to discuss how to deal with the flu, and they are postponing their flight to Kansas City from Thursday to Friday. That will allow the players to get an extra day of rest at home and one day away from each other to limit their exposure. Teams normally fly to another city the day before the series opener.
"We're not the first pro sports team to have to deal with the flu," general manager Jon Daniels said.
"I'm sure I will [get sick]," said outfielder Josh Hamilton. "Not yet."
The remaining healthy players covered their noses and mouths with anything they could find to avoid getting sick.
"I'm overall weak and nauseous," Murphy said. "Mine doesn't seem severe, but it doesn't get worse."
Washington hoped Nippert would give his team 70 pitches over four or five innings on Wednesday night. Every reliever is available except Guardado and C.J. Wilson, who has pitched the last three nights. Washington said he wouldn't consider using Wilson in any situation.
Francisco was placed on the disabled list on July 20. Because the move was retroactive to July 11, he is eligible to come off on Sunday.
Vizquel was scratched from last night's lineup with a 103-degree fever that came on quickly before the game. Eyre said he got sick after getting home last night, and he couldn't stop coughing.
Daniel Paulling is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.