Fraley, who missed Friday's game, has a stress fracture in the fourth toe on his left foot. He is hitting .263 with an .813 OPS and 15 home runs, 63 RBI and 20 stolen bases this season.
The move is retroactive to Friday.
Fraley also was sidelined during the 2022 season with a toe injury suffered during his rehab while out with a knee issue.
Cincinnati has lost its last four games to fall out of the lead in the National League Central entering Saturday's games, with the Milwaukee Brewers ahead by a half-game.
The Reds on Saturday also recalled outfielder TJ Hopkins from Triple-A Louisville to take Fraley's spot on the roster. He made his major league debut earlier this season, going 4-for-24 with a stolen base in 14 games.
Greene, 23, last pitched in a major league game June 17. He was 2-4 with a 3.93 ERA in 14 starts this season and is 7-17 with a 4.25 ERA in 38 career starts over the last two seasons for the Reds. He has 264 career strikeouts over 199 innings.
Gutierrez, 27, underwent Tommy John surgery last year. He was 1-6 in 10 appearances (eight starts) for the Reds last season and had a 7.61 ERA.
Reuters contributed to this report.