Arquimedes Caminero, another hard-throwing reliever, was recalled from Triple-A New Orleans to take Capps' roster spot.
After experiencing some tenderness on Sunday, Capps didn't make the trip to Washington. He remained back in Miami, and underwent an MRI, which revealed the sprain.
The preliminary prognosis is four weeks of rest before Capps is cleared to throw. The hope, at this point, is that surgery can be avoided.
"We feel like right now, it's something that can be treated with rest," manager Mike Redmond said. "He's going to go four weeks without throwing. He will be down for an extended period of time, and then building back up, and we'll go from there."
Capps threw one inning on Sunday in a 7-1 loss to Milwaukee at Marlins Park. The right-hander allowed one run on two hits with a walk and a strikeout.
Velocity was not an issue during the appearance, as he struck out Ryan Braun to end the inning. One of Capps' fastballs during Braun's at-bat was clocked at 99 mph. He was regularly throwing 97-plus mph.
The 23-year-old maxed at 101 mph earlier in the season.
Capps, who opened the season with New Orleans, became an effective late-innings option after being called up in late April. In nine appearances for Miami, he had a 3.00 ERA, and struck out 15 while walking three in 12 innings.
Miami acquired Capps from the Mariners last December for outfielder Logan Morrison. Redmond has been searching for reliable relievers for the seventh and eighth innings, and Capps, a converted catcher, was in the mix. Now, Caminero has a chance to step up.
"We need him to come up and throw strikes and get guys out and be able to log some big innings," Redmond said. "Hopefully, he has the confidence to go out there, and he has been pitching better. Hopefully, he can go out there and get some big outs for us at a time we need him."
Capps worked in Spring Training on adjusting his delivery, which is one reason he didn't make the Opening Day roster. The club opted to let him iron out his mechanics with New Orleans.
He impressed in seven Triple-A appearances, striking out 17 and walking just six in 11 innings.
News of Capps' elbow sprain came on the same day Jose Fernandez returned to Los Angeles to have his cast and stitches removed from his Tommy John elbow surgery.
When Fernandez was placed on the disabled list earlier this month, he was listed as having a right elbow sprain.
Caminero is making his second stint with the Marlins. The right-hander has appeared in five games, giving up seven runs in 4 2/3 innings. He threw 19 innings in 11 appearances for New Orleans. His record was 1-1 with a 6.63 ERA.
"I was getting better before they called me," Caminero said. "They wanted to see if I could throw multiple innings there, and I showed them I can."