Alvarez, who started the season on the disabled list with right shoulder inflammation, has been building up for game action. Recently, he was facing batters, and the next step was going to be rehab-assignment games.
Now, there is no telling when Alvarez will begin throwing.
"He's going to be down," Redmond said. "He's taking a break."
Alvarez's setback comes at a time the Marlins welcomed shortstop Adeiny Hechavarria back from the 15-day disabled list.
Redmond added that catcher Jeff Mathis, who fractured his right collarbone early in Spring Training, began his rehab-assignment stint on Thursday. He was scheduled to play five innings for Class A Jupiter.
Alvarez, Hechavarria and Mathis were part of the blockbuster 12-player trade between the Marlins and Blue Jays in November.
Actually, both teams have dealt with injuries in the trade. Josh Johnson and Jose Reyes are on the DL for Toronto.
On the Marlins' end, Alvarez, Mathis and Hechavarria have spent time on the DL. So has Minor League outfielder Jake Marisnick (broken left hand). Marisnick currently is playing for Double-A Jacksonville.
Joe Frisaro is a reporter for MLB.com. He writes a blog, called The Fish Pond. Follow him on Twitter