Rodriguez, who has converted 10 of 11 save opportunities including his last seven, doesn't think the problem is serious.
"I don't think there's any damage to the ligament," he said. "I think it's just the muscle."
"It's nothing long-range to be concerned about," said Angels manager Mike Scioscia. "It looks like there's a little stiffness, but we want to get it out of there. We're going to err on the side of caution."
Asked if Rodriguez would be able to pitch in the remaining two games of the series, Scioscia said, "I'm not going to rule it out. We'll take a look (Tuesday)."
According to Scioscia, Rodriguez told the Angels the forearm was bothering him after pitching in the first game of Saturday's doubleheader in Detroit. He said he was unavailable before Sunday's game and was examined by Tigers team doctors.
Rodriguez had an MRI which confirmed the strain Monday in Cleveland. Rodriguez, who had an ice pack on his forearm in the trainer's room, was examined by Indians team doctor Mark Schickendantz on Monday evening. Rodriguez will be re-evaluated by Angels team doctor Lewis Yocum when the team returns to Los Angeles on Thursday.
Right-hander Scot Shields will take over the closer's role while Rodriguez is out.
Rodriguez is 1-1 with a 2.25 ERA in 14 appearances. Opposing hitters are batting .164 against him, and he has struck out 23 and walked two in 16 innings.
Steve Herrick is a contributing writer for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.