Two-time American League Cy Young winner Corey Kluber could be done for the season after only one inning for the Texas Rangers.

He has a tear in a small muscle in his right shoulder that won't require surgery, but even in the best-case scenario in this shortened season, he won't throw again for at least four weeks, which is when he will be evaluated again.

"It's a blow -- there's no getting around it," Jon Daniels, the team president and general manager, said Monday.

Daniels said an MRI revealed a grade 2 tear. The 34-year-old right-hander will receive a platelet-rich plasma injection this week.

"Given the time frame here and the nature of a 60-game schedule and everything that goes with it, the timeline is not on our side," Daniels said. "We will give him his period to rest, and then if it's recovered, or the injury is healed to the point where he can begin throwing, he'll do so with the potential to possibly be ready for the end of the season. If that is the case, it'd probably be more likely as a reliever, given the time needed to build up as a starter."

The Rangers didn't immediately make a roster move Monday since they had the day off, but Kluber is headed to the injured list. Daniels said young left-hander Kolby Allard, who is already on the 30-man roster after nine starts as a rookie last season, will fill Kluber's spot in the rotation.

Kluber exited Sunday's home game against Colorado after one scoreless inning with tightness behind the shoulder. It was his first start in the majors since May 1, 2019, when he broke his right forearm on a liner to the mound. He injured his side during rehab last summer.

The Rangers acquired Kluber in a trade from Cleveland in December, adding him to a rotation with All-Star left-hander Mike Minor and hard-throwing veteran Lance Lynn.

"I felt like he was in a really, really good spot, had had really no physical issues at all," Daniels said. "Talking to him a little bit today, he feels better than he's felt in years physically. Really no indication that this was coming. He was throwing the ball really well."

Texas has an $18 million club option for 2021, and Daniels said it was too early to think about that. But the GM did say the Rangers acquired Kluber with the mindset to have him beyond the season, adding that the setback doesn't necessarily change that desire.

Kluber was Cleveland's Opening Day starter each of the past five seasons, part of a stretch when he was one of baseball's most dominant and consistent pitchers. Before getting hurt last season, he was a 20-game winner in 2018, had thrown at least 203 innings with 222 strikeouts each season from 2014 to 2018, and was the Cy Young winner in 2014 and 2017.

Kluber spent nine seasons in Cleveland, and Indians manager Terry Francona texted the pitcher warm wishes and support Monday.

"Just telling him that I'm thinking about him," Francona said. "That's tough. He's really run into some tough luck. He was coming back last year and the oblique got in the way. ... I don't care who they're with, or they're not with you anymore. Whatever the circumstances, you certainly feel for that. That doesn't make anybody feel good."