The procedure on Greene's non-throwing elbow was performed in Dallas by Texas Rangers team physician Dr. Keith Meister.
The Tigers anticipate Greene, the fifth overall pick in the 2019 amateur draft, will be ready by the start of next season.
The 22-year-old batted .288 with 11 homers and 37 RBI in 99 games in his second major league season. He missed 34 games earlier in the season due to a left fibula stress reaction.
Manager A.J. Hinch said before Wednesday's game against the Los Angeles Dodgers that he doesn't want Greene to change his aggressive approach despite a run of injuries.
"I know what's in his heart and DNA and how he is going to continue to make plays," Hinch said. "He has been on the unlucky side of these injuries and some have been worse than others. We will try to figure out the best way to keep him healthy over the long term."