The Reds also recalled right-hander Connor Phillips, who made his third career start Monday night against the Minnesota Twins and earned his first win. Phillips allowed two runs off a pair of homers but struck out seven in seven innings.
It's unclear when Bader suffered the injury. He played Sunday, starting in center field and going 0-for-3 before being replaced in the seventh inning. He has started nine of 14 games for the Reds since they claimed him off waivers last month from the New York Yankees.
Bader is batting just .161 for the Reds and .232 overall this season. He has seven home runs on the season but none with the Reds.
Also Monday, the Reds designated outfielder Hunter Renfroe for assignment and activated outfielder Stuart Fairchild from the seven-day injured list.
Renfroe, 31, was claimed off waivers from the Los Angeles Angels and played 14 games with Cincinnati, during which time he hit just .128. Renfroe has 20 home runs this season, all but one with the Angels.
Fairchild, 27, hit .223 with five home runs and 27 RBIs through 88 games with the Reds this season.
The team also reinstated LHP Alex Young from the COVID IL and optioned RHP Carson Spiers to Triple-A Louisville.
Young is 4-2 with a 3.31 ERA in 57 relief appearances for the Reds.
Phillips, 22, is 0-0 with an 8.31 ERA in two starts this season, both in September.
To make room for Phillips on the 40-man roster, the Reds transferred RHP Graham Ashcraft to the 60-day IL.
Reuters contributed to this story.