Fuentes hadn't pitched since Opening Day due to stiffness in the middle of his back. The move is retroactive, meaning Fuentes will be eligible to return April 21 when the Angels face the Detroit Tigers.
Fernando Rodney, who went 37 for 38 in save opportunities with the Tigers last year, will be the Angels' interim closer. The Angels signed Rodney to a two-year, $11 million contract last winter in part because of his experience as a closer.
"I think this isn't a huge adjustment of roles for guys," Angels manager Mike Scioscia said.
Angels relievers thus far rank 11th in the American League with a 5.68 ERA and have blown three saves. Rodney has struggled early, having allowed four runs in his first three innings.
"I did well last year and I'll try to do well this year, too," Rodney said. "I'm always ready."
Fuentes injured himself while lifting weights April 6, but said he expects to return when he's eligible. On Opening Day against the Minnesota Twins, he picked up his first save with a perfect ninth inning.
Fuentes led the American League with 48 saves last year. He has to finish 55 games this season in order for a $9 million option for next season to vest.
"We tried to kind of wait it out, but it wasn't getting any better," Fuentes said.
The Angels recalled recalled reliever Francisco Rodriguez from Triple-A Salt Lake to fill Fuentes' spot on the 25-man roster.
Mark Saxon covers the Angels for ESPNLosAngeles.com