Theriot had been playing through the nagging injury, but an MRI on Friday revealed a more serious problem. In 24 May at-bats, Theriot had just two hits.
"It goes back to Spring Training," Giants manager Bruce Bochy said of the elbow. "It got better, then we found the sprain today."
Loux last pitched in the Major Leagues with the Angels in 2009, when he made 18 appearances and had a 5.86 ERA over 58 1/3 innings.
In Fresno this season, Loux was dominant out of the bullpen. In 21 innings, he allowed just one earned run, with batters hitting .157 against him.
Even more attractive to the Giants is that Loux is able to throw multiple relief frames at a time. Of his 13 appearances this season, only four of them were for one inning or less.
"We need someone to give us multiple innings," Bochy said. "We're better off going with 12 pitchers. He was throwing the ball well."