The Reds also said they moved RHP Johnny Cueto to the 60-day disabled list to open a roster spot for right-hander Nick Christiani, who was called up from Triple-A Louisville.
Broxton left Wednesday's 10-7 win over Arizona after facing two batters in the eighth inning. The appearance was his fifth since being activated on August 7 following almost two months on the disabled list with a strained right elbow.
Cueto is in his third DL stint this season with a strained muscle behind his right shoulder. He hasn't pitched since June 28. Christiani is 6-5 with a 4.05 earned-run average and three saves in 47 games with Louisville this season. He has yet to make his major league debut.