The lefty had been tentatively considered to start the Sunday finale against Cincinnati at PNC Park.
Manager Clint Hurdle was not yet prepared to name a replacement starter for Rodriguez -- or to definitely rule him out.
"We're gonna give Wandy another rehab work day," Hurdle said after Wednesday's game. "We'll get him out to the park Friday, and should have a decision sometimes that afternoon or evening."
If he can't go, candidates for that spot start include pitchers on the current staff -- Jeanmar Gomez, Chris Leroux or Justin Wilson -- or someone being recalled from Triple-A Indianapolis.
Tom Singer is a reporter for MLB.com and writes an MLBlog Change for a Nickel. He can also be found on Twitter @Tom_Singer. This story was not subject to the approval of Major League Baseball or its clubs.