Capps hopes to return over the weekend, but "it's kind of out of my hands," he said.
The 25-year-old right-hander experienced some numbness and tingling after Geovany Soto's shot up the middle hit him with one out in the ninth, but was relieved after X-rays showed no structural damage.
"I don't know what other tests they'll do from here," Capps said. "I'm sure it'll depend on how I feel. The biggest thing right now is keeping the inflammation out of it and trying to get the range of motion back."
Manager John Russell added: "We'll just see how it responds."
Sean Burnett relieved Capps and got the final two outs to preserve Pittsburgh's 10-8 victory.
Capps, who has converted nine of his 11 save attempts, struck out the side the previous day while finishing off a 4-3 victory over the Chicago White Sox.