Parra is in the final season on a two-year, $5.5 million contract. He could still be dealt after the Deadline, but would have to clear waivers.
During Sunday's 5-3 loss to the Indians, Parra threw 31 pitches over 1 2/3 innings. He allowed two hits and walked a batter with the bases loaded to give up an inherited run. After last season, he had surgery to debride, or clean out, the same elbow.
"It was a new to the injury report postgame. He was experiencing soreness there in [his] second inning, which we didn't know about until afterwards," Reds manager Bryan Price said. "Especially with the doubleheader coming up [Wednesday], we just couldn't, even with an eight-man bullpen, cover a 7-15 day absence."
This marks the second time Parra has gone on the DL this season. He also was out from April 29-May 25 with a neck strain.
In 18 games, including 17 starts, this season for Louisville, Axelrod is 6-6 with a 4.05 ERA. Over 97 2/3 innings, he's allowed 105 hits, 11 homers and 25 walks with 61 strikeouts.
On Thursday, Axelrod was transitioned to a long-relief role at Louisville and pitched three innings.
"They told me that day I was going to be in the bullpen, and I pitched that day. Now, here I am. It was kind of interesting," Axelrod said.
Axelrod was up with the Reds last season, going 2-1 with a 2.95 ERA over five games (four starts). Aware that his role isn't an easy one, he is anticipating anything that may happen and is ready for the bullpen phone to ring.
"You have to be ready every day, pretty much from the first inning, on. If anything happens, you're the guy," Axelrod said. "You kind of just have to be on your toes at all times. Even at the end of the game when things get out of hand or go to extra innings, you have to be ready. There aren't many times you can get let your guard down."
The Reds announced that left-hander Tony Cingrani would be activated from the 15-day disabled list on Wednesday to start the second game of a doubleheader against the Cubs. Cingrani has been on the DL since June 15 with a strain in his left shoulder.
In four rehab outings, including three starts for Triple-A Louisville, Cingrani worked 14 scoreless innings with six hits, six walks and 18 strikeouts. He threw 93 pitches over five innings on Friday. Moved to the Reds' bullpen before the season, his last big league start was on June 9 against the Dodgers.