Darvish is scheduled to start again Tuesday against the Tampa Bay Rays.
The 26-year-old Darvish experienced discomfort in his quad while throwing a bullpen session at Rangers Ballpark in Arlington on Tuesday and received treatment.
Darvish told manager Ron Washington and pitching coach Mike Maddux that he could start if necessary, but the club decided to rest him anyway.
"You can't take that type of chance," Washington said. "We decided to just skip him until his next turn."
Darvish was doing some light jogging in the outfield before batting practice on Wednesday to test the injury, which isn't considered serious.
"I just felt a little tightness in my quad during my bullpen yesterday," Darvish said in a statement. "I don't look at it as an injury, just a precaution. It's just a small problem now. I want to handle it before it becomes a big problem. We talked it over with the coaches, and this is the best decision for me and the team going forward."
Darvish has not missed a start all season because of injury. The club did decide to skip his final start before the All-Star break to give him more time to rest before the second half of the season.
The rookie pitcher from Japan is 12-9 with a 4.51 ERA with 80 walks and 172 strikeouts. He entered Wednesday second in the AL in walks and fourth in strikeouts.
Darvish's past two outings have been quality starts. He is 1-1 during that span, including a solid showing in Toronto on Friday. Darvish allowed three runs on just three hits with 10 strikeouts and one walk against the Blue Jays, but got the loss as the Rangers fell 3-2. It was just the second time in 23 starts that Darvish had fewer than two walks.
Oswalt will be making his eighth start of the season on Thursday. He allowed one run on two hits in 4 2/3 innings on Saturday in Toronto, falling one out shy of the win. He is 4-2 with a 6.04 ERA in 10 appearances (44 2/3 innings) with the Rangers.
Oswalt threw a bullpen session during Tuesday night's game so he'd be ready if needed Thursday.