"It's definitely a concern anytime you have one of your star pitchers go down and have something sore," Manager Mike Redmond said. "We'll just have to monitor him as we go. … It's tough not having him, for sure."
Alvarez (0-2) sat out the first half of the 2013 season because of shoulder inflammation. He had a stint on the disabled list last August because of a shoulder issue.
Alvarez was 12-7 with a 2.65 earned-run average last year and was an All-Star.
Miami also put backup catcher Jeff Mathis and reserve infielder Don Kelly on the 15-day disabled list. Each broke the ring finger on his right hand in Sunday's game.
Also, right-hander David Phelps was put on the paternity list after his wife gave birth. He is expected to rejoin the team Thursday. Redmond said Phelps is the probable choice to replace Alvarez in the rotation on Friday.
LaTroy Hawkins is out as Rockies closer
LaTroy Hawkins is being moved out of Colorado's closer role for now, but Manager Walt Weiss isn't ruling out the right-hander returning to ninth-inning duties.
Weiss called it a "breather" for Hawkins, 42, who is planning to retire after this season.
"We'll do that for the time being," Weiss said. "We'll mix and match. We have some pieces that can pitch late. The stuff is still very much intact with Hawk. We'll give him a little breather."
Hawkins blew a save opportunity in Colorado's 6-5 loss to the Chicago Cubs on Sunday at Coors Field, surrendering a two-run home run to former Rockies outfielder Dexter Fowler with two outs in the ninth.
Rob Manfred comments on MLB's latest drug suspensions
Commissioner Rob Manfred says Major League Baseball is investigating four recent positive tests for the steroid Stanozolol along "the same model" as its 2013 Biogenesis probe.
Injured New York Mets closer Jenrry Mejia was suspended for 80 games Saturday, the fourth player in 16 days banned under the major league drug program after a positive test for Stanozolol, a steroid popular with body builders.
Mejia's discipline came after positive tests and suspensions for Minnesota pitcher Ervin Santana, Seattle pitcher David Rollins and Atlanta pitcher Arodys Vizcaino.
Manfred said baseball will work to determine whether there is any link among the four cases.