Marlins manager Don Mattingly announced the decision, which he clarified was not that of the 27-year-old right-hander.
The Marlins will miss the postseason, sitting fourth in the NL East with a 66-92 record.
Alcantara is among the NL Cy Young favourites along with Zach Gallen, Julio Urias and Max Fried.
Alcantara (14-9) has been a standout, with a 2.28 ERA over 32 starts, leading the majors with 228-and-two-thirds innings. He has struck out 207 and walked 50 batters.
"Sandy was, obviously, he's one of those guys that wants to keep going," Mattingly said. "We got to do the best thing for Sandy, and we felt like this was it."
"It's pretty incredible really what Sandy's been able to do. There's no reason to have him continue this year. We got to take care of Sandy first."
Meanwhile, New York Yankees veteran reliever Zack Britton has been placed on their 60-day injured list after failing in his early return from Tommy John surgery.