Phillips suffered his injury while making a sliding catch in the eighth inning of Wednesday's game against the Chicago Cubs. He wore a splint as he left the clubhouse.
Phillips, 33, has hit .272 with 19 doubles and seven home runs in 86 games this year.
The Reds promoted infielder Kris Negron from Triple-A Louisville after injuries to center fielder Billy Hamilton (hamstring) and Phillips.
In Thursday's game, Reds right-hander Homer Bailey left his start against the Cubs in the sixth inning with pain in the patellar tendon of his right knee.
Bailey was delivering a 1-2 pitch to Starlin Castro, but he didn't throw the ball while gingerly completing his motion. After a visit from trainer Paul Lessard and manager Bryan Price, he walked off the field and was replaced by the right-hander Sam LeCure.
After the game, it was announced that Bailey has a slight knee strain and is expected to make his next start.
Negron, 28, has hit .269 with three home runs with Louisville. He appeared in four games with the Reds in 2012, but that is his only major league experience.
The Reds optioned right-hander Carlos Contreras to Louisville to make room on the 25-man roster for Negron. Louisville right-hander Brett Marshall was designated for assignment to make room for Negron on the 40-man roster.
Contreras appeared in three games out of the bullpen for the Reds, allowing one run in 4 1/3 innings.