Garrett, the seventh overall pick in the 2016 MLB Draft, was off to a promising start at Class A Greensboro. The 19-year-old left-hander posted a 1-0 record with a 2.93 ERA in four starts and 15 1/3 innings.
"Obviously, you wanted to get him out into his first full season, and continue on his development program," Hill said. "He was off to a good start, was throwing well. We know, unfortunately, it's part of the game. We'll get it addressed now, get him back in 12 to 14 months and continue his professional career."
At a time when the Marlins are prepared to be without Garrett, Miami is close to reaching an agreement with the club's first-round pick in the 2017 MLB Draft, left-hander Trevor Rogers from Carlsbad High School in New Mexico.
Hill said Rogers could be announced by the end of the week, after he completes his physical.
The Greensboro rotation also suffered another setback, as hard-throwing right-hander Jordan Holloway also underwent Tommy John surgery on Monday.
Garrett and Holloway, ranked 14 by MLBPipeline.com, have a chance to be in the same rotation with the Marlins in a few years.
"I want to get them healthy so they're ready for this rotation," Hill said of the big league staff. "Unfortunately, it's part of it."
The Greensboro rotation could be adding a power arm in a couple of weeks. Tyler Kolek, the club's No. 2 prospect, is pitching in extended spring games. Kolek had Tommy John surgery in 2016, and will eventually join Greensboro.
"He's looked really good," Hill said of Kolek. "I jumped up there to Jupiter to see him throw. Smoothed out his delivery. Not worried about velo. Delivery looks good and it's coming out hot. My eye radar says it looks good. That's all I really care about."