Price estimated that the back has been an issue for Parra for "maybe three days."
Parra was also quietly held out for a 10-day stretch last month with left shoulder soreness.
"The shoulder is feeling good," Price said.
Meanwhile, injured right-handed reliever Logan Ondrusek resumed a throwing program on Tuesday when he played catch on the outfield grass. Ondrusek has been on the disabled list with a strained right shoulder since July 22 (retroactive to July 13).
Price was glad that Ondrusek was ready to throw again after he had been shut down for several days.
"He still had just a bit of soreness [Monday], so that's a good sign," Price said. "There will be a throwing protocol. He's going to have to take some steps as far as effort level, long toss and bullpen to be able to sign off on reactivation. If we activate him and he's sore in his first outing, we have to put him back on for 15 days."
Mark Sheldon is a reporter for MLB.com. Read his blog, Mark My Word, and follow him on Twitter @m_sheldon. This story was not subject to the approval of Major League Baseball or its clubs.