The 26-year-old left-hander was placed on the 10-day injured list Thursday and will have arthroscopic surgery to remove loose bodies from his pitching elbow. Team orthopedic surgeon Dr. Koco Eaton will perform the procedure Monday, and the Rays anticipate Snell will be ready to return in September.
An industry source told ESPN's Buster Olney that Snell is expected to miss about six weeks. However, it's possible the time frame could be longer, the source said, because so much will be dependent on where the Rays are in the playoff race.
Through Wednesday's games, the Rays (58-47) trail the first-place New York Yankees by 10 games in the AL East and are just one game behind the Oakland Athletics (58-45) for the final spot in a competitive AL wild-card race.
If Snell's rehabilitation is seamless and the Rays are in a pennant fight, Snell might return to the rotation in early- to mid-September. If the Rays fall out of the race entirely, Tampa Bay would have the option of giving Snell more recovery time or even deferring his return to the spring of 2020.
Snell said he's confident the Rays can remain in playoff contention while he's out.
"With the team we have, I know they're going to ball out. I'm not worried about them," said Snell, who became the second Cy Young winner in franchise history last season, when he led the major leagues with 21 wins.
The 26-year-old lefty is 6-7 with a 4.28 ERA and 136 strikeouts in 20 starts this season, including 2-0 with a 1.64 ERA in outings since June 30.
Snell, who signed a $50 million, five-year contract during spring training, said he initially felt discomfort in his arm "three or four starts ago" and became more concerned while playing catch Tuesday. He had an MRI following a bullpen session Wednesday.
"I was upset," Snell said of his reaction to learning he would need surgery. "Felt like this whole year has kind of been that way. ... Every time I found my groove and felt like I was about to get going, something had to get in the way. Just very frustrating."
He becomes the latest talented Rays pitcher to hit the injured list, joining right-hander Tyler Glasnow.
The Associated Press contributed to this report.