Vargas left his start against Pittsburgh on Tuesday night after throwing just 26 pitches. He had an MRI on Wednesday that revealed the extent of the injury.
"The report didn't come back good," Royals manager Ned Yost said. "He's definitely going to have to have surgery. He's going to be out for a while. I mean, it's a 12- to 14-month recovery. The good thing is, when he comes back he'll be every bit as good as he was before he got hurt."
Vargas had been on the disabled list twice previously this season with elbow injuries and had just returned from the DL on Tuesday.
"But he did a really good job of rehabbing it back," Yost said. "He looked great in his sim games. He looked good in his rehab start. He looked phenomenal last night in the first inning with two punchouts, throwing his fastball 88 miles per hour and down in the zone. His command was great with his changeup and his fastball. It's just one of those things that just went."
The Royals filled Vargas' spot in the rotation by recalling Yordano Ventura, who had been sent to Triple-A Omaha just a day earlier to work on his inconsistency and rebuild some confidence after a string of poor starts. Ventura was the team's Opening Day starter.
"Is it beneficial to go to a lower-key environment for a start or two and have some success? Yeah," Yost said. "But this kid has had some success at the major league level. Hopefully he'll get better and better as the second half goes on."
Ventura will start Sunday against the Astros.
Vargas, who is 5-2 with a 3.98 ERA, was instrumental in the Royals' run to the World Series a year ago. He went 1-0 with a 3.52 ERA in three postseason starts. Vargas, 32, is in the second year of a four-year, $32 million contract, with the Royals owing him $16.5 million for 2016-17.
Ventura, 24, is 4-7 with a 5.19 ERA in 14 starts this year.
The Associated Press contributed to this report.