The exact nature and date of the surgery were not known.
Meche threw for Triple-A Omaha in an injury rehabilitation appearance on Monday and gave up seven runs in four innings.
"It didn't go real well," said Yost. "He's still experiencing some pain in his shoulder and so our next move is that he'll probably go and have some surgery on it to figure out exactly what's wrong and repair it.
"That's probably going to be the next step. We're still evaluating but it looks like that's probably what we're going to have to do."
Meche has been on the disabled list with what was originally listed as right shoulder bursitis since last pitching for the Royals on May 25.
"When he gets in and is evaluated fully by the doctor, I imagine it'll be some type of cleanup in there with the scope," Yost said. "He still has irritation and it's not getting better so we're looking at probably scoping it and getting it cleaned up and having him ready for next year."
Meche came out of a Cactus League game in Arizona on March 22 after three innings with shoulder tightness. He worked his way back and his first start of the season was delayed until April 9.
This would be the second straight year that Meche's season has ended early. In 2009, back problems kept him from starting after Aug. 29. An iron man in his first two seasons with the Royals, he was limited to 23 starts and had a 6-10 record and 5.09 ERA.
"He's a little down right now," Yost said. "He worked really hard to do everything he could do to get back without having this happen but common sense says you can fight this and fight it and fight it but you get to the point where you have surgery later and that jeopardizes what we need him for next year. So go ahead and get it done as soon as we can and hopefully have him ready to go next year."
Meche made just nine starts this season and was 0-4 with a 6.66 ERA.
"He came and pitched effectively at times during the season," Yost said. "This is almost kind of like a last resort thing. We exhausted every other option that we could do so that we wouldn't have to come to this. But this is what it's come to and we have to move forward with it.
"It's always a blow when you lose a guy that has the capability to win games like Gil does but you fix it and you move on."
Meche next season will be in the last year of his original free agent five-year, $55-million contract with the Royals.
On the upside, disabled starter Luke Hochevar (right elbow sprain) had a good throwing session on Monday. He's been out since June 12 and, at the moment, there's no target date for him to return to throwing off the mound.
"But it'll be very soon," Yost said.
Dick Kaegel is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.