An official roster move was not made and Price and the club plan to name Bailey's replacement on Friday. The club played a man short on its 25-man roster Thursday.
Bailey was originally bumped back from a Wednesday starting turn because of elbow stiffness that stemmed from swinging a bat in his previous start on Aug. 7 against the Indians.
The Reds and Bailey were optimistic that he could make the Saturday start until he played catch on Tuesday and still didn't feel right.
"What happened was it didn't get any better. At one point, he felt like he had taken a step backwards," Price said.
An MRI exam on Wednesday revealed the injury. Bailey did not travel to Denver with the club and remains in Cincinnati.
"It certainly means there will be a week of no throwing and then we'll reassess," Price said. "He'll start to play catch. How quickly he bounces back will directly correlate with how quickly we get him back."
The flexor mass injury is similar to one fellow starting pitcher Mat Latos endured during an April setback as he tried to return from elbow and knee surgeries. It did not require surgery and Latos was back pitching in June. Last August, reliever Jonathan Broxton experienced a flexor mass tendon tear and had season-ending surgery.
Bailey, who signed a six-year, $105 million contract in February, is 9-5 with a 3.71 ERA in 23 starts this season. In four starts since the All-Star break, he is 1-0 with a 1.61 ERA.
On the Reds' 40-man roster, Triple-A Louisville's David Holmberg pitched on Wednesday and will not be available for Saturday. The best bet for the start could be right-hander Dylan Axelrod, who last pitched on Monday for Louisville and would be on regular rest for Saturday.
Axelrod, 29, appeared in 48 games -- with 30 starts -- for the White Sox from 2011-13 and had a 5.36 ERA. The Reds purchased his contract from Chicago on July 17. He is 2-1 with a 3.06 ERA in five starts since joining the Bats and worked a two-hit shutout to defeat Rochester on Aug. 5. On Monday, Axelrod worked 7 2/3 innings with four runs allowed for a win against Scranton-Wilkes Barre. He is not on the club's 40-man roster.
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.