Wood was scheduled to pitch, but was unavailable on Saturday.
"He has a little spring soreness and just didn't feel ready today," manager Manny Acta said. "He'll be ready in a few days."
Wood made 12 trips to the disabled list with various arm ailments and surgeries in 11 years with the Chicago Cubs. He signed a two-year, $20.5 million deal with Cleveland in December 2008, worked in 58 games in 2009, and is 1-0 in two scoreless innings this spring.
Cleveland also was without shortstop Asdrubal Cabrera, out with a strained left groin. Texas second baseman Ian Kinsler sat out with a sprained right ankle. Both got hurt Friday and are expected to be sidelined at least a week.
McCarthy, competing for a Rangers rotation spot, allowed three hits, one walk and struck out three.
"I really wanted to work on the cutter and threw some for strikes," McCarthy said. "Now, I've got to shore up the curveball and the change. I'll work on that this week."
McCarthy went to the bullpen to throw 15 more pitches, getting his total up to about 50.
"I need to throw pitches down and away consistently," he said. "So I threw some more to work on that."
McCarthy consistently got ahead in the count for two innings. Rookie Carlos Rivero doubled to open the third and Michael Brantley walked on four pitches, but the right-hander quickly got out of the jam.
"I kind of lost the zone and had to right the ship," he said. "I got out of the inning, but went down to the bullpen to find it again."
McCarthy missed the second half of 2009 with a stress fracture in his right shoulder -- making his fifth trip to the disabled list since being acquired from the Chicago White Sox before the 2007 season.
Indians starter Justin Masterson struck out six over 3 2/3 innings. The right-hander, already selected to the rotation, gave up three hits, one walk and an unearned run.
"I was ready to keep going when Manny came and got me," Masterson said. "I'd rather feel like that than it being, 'please come and get me'."
Masterson, working on a changeup to complement his sinker, was pleased with the few offspeed pitches he threw.
"The sinker was really moving, but the change felt good, too," he said.
Acta was very happy.
"Masterson was the highlight of the day for us," he said. "He missed some bats."
Former Indians manager Frank Robinson visited with Acta, who succeeded the Hall of Famer as Washington Nationals manager in 2007. ... Indians 1B Russell Branyan has yet to play as he rehabs from a herniated disk in his back. Branyan said he "hopes to play a little catch" Sunday. ... Veteran RHP Jason Grilli, on a minor-league contract with Cleveland, is out for the season. He will have surgery next week in Vail, Colo., by Dr. John Steadman on a torn right quadriceps, sustained while running on March 5. ... Texas claimed INF Hernan Iribarren on waivers from Milwaukee and placed RHP Eric Hurley on the 60-day disabled list. ... Rangers players talked about entertainer Charlie Pride's annual visit to their camp. Pride, who turns 72 on March 18, sang some country tunes and told baseball stories. Pride was a pitcher in the Negro leagues and Yankees farm system in the early 1950s.