Manager David Bell said the shoulder had popped from time to time this season but was more noticeable his last time out, when he held the Marlins to just a hit while striking out eight without walking a batter over six scoreless innings.
"We thought he was going to be fine and he even threw a bullpen today and that's when he felt it a little bit more than normal," Bell said.
Greene, who turns 23 on Saturday, seemed to be turning the corner in his young career over the last month, posting a 2.70 ERA over his last four starts with 29 strikeouts and eight walks over 23 1/3 innings.
"It is what it is," Greene said. "It's part of the game. It is frustrating to have to deal with it. Definitely looking toward the positives to getting back as soon as possible."
The rookie has started 20 games for Cincinnati this season, posting a 4-12 record and 5.26 ERA. He's struck out 127 batters in 102 2/3 innings.
"It's serious enough to go on the IL but hopefully no more serious than keeping him out for 15 days, then having him back so he can finish out his first season here strong," Bell said.
Right-handed reliever Ryan Hendrix was recalled from Triple-A Louisville to fill Greene's spot on the active roster but Bell has yet to name who will replace Greene when his spot in the rotation comes up again on Sunday.