Alvarez underwent a season-ending operation in May and is not expected to pitch until at least a month into the 2016 season.
"A very difficult decision," president of baseball operations Michael Hill said. "But as we looked into the offseason, we are going to need depth, and we're going to need innings. He's not going to be able to provide those for us for some time."
Alvarez has just started playing catch, the latest step in his rehabilitation, Hill said. Alvarez was an All-Star in 2014 and the Marlins' Opening Day starter this year, but he made only four starts in 2015 and lost them all.
In 2014, Alvarez went 12-7 with a 2.65 ERA in 2014. He was expected to command about $4 million through arbitration, and the cost-conscious Marlins decided they couldn't afford that.
"Given our challenges, we have to have our dollars on the field performing for us," Hill said.
The Marlins also non-tendered reliever Aaron Crow, who is recovering from Tommy John surgery. Miami tendered right-handers Jose Fernandez, A.J. Ramos, Tom Koehler, Bryan Morris, David Phelps and Carter Capps, second baseman Dee Gordon, and shortstop Adeiny Hechavarria.