The moves are retroactive to May 19.
Alonso has a sprained right hand, and Hunter is experiencing lower back pain. Alonso has been nursing the injury since he was hit by a pitch more than two weeks ago.
"I want to nip this in the bud,'' he said. "This is something where I feel like if I address this now, I'm going to be completely healthy the rest of the season. If we want to win the war, I've got to get right.''
The move was made before the start of the Mets' weekend series at Miami. Alonso said he hopes he can return as soon as he is eligible to come off the IL.
Alonso is hitting .236 with six home runs and 19 RBIs this season. Hunter has made four appearances, with one start, and has not given up a run in eight innings of work.
The Associated Press contributed to this report.