Such injuries usually sideline a player for a long period. Moustakas said he will seek a second opinion on the injury.
"We're still talking with the doctor, get a second opinion, see where we're at," Moustakas said. "You can't rule anything out. I just want to go out there and be healthy and get prepared to play baseball again. That's where I'm at right now."
General manager Dayton Moore said surgery is a likely option.
"Obviously, it's looking more like that, but you hate to jump the gun on that," Moore said. "You need to just let it take its course, get second opinions, go from there and see what happens."
Moustakas and left fielder Alex Gordon collided Sunday while chasing a fly ball in Chicago. Gordon went on the disabled list Monday with a right wrist fracture.
"It's disappointing. It's just one of those things that happen in sports," Moustakas said. "You can't control everything. Me and Gordo [Alex Gordon] are going out trying to make a play and unfortunately we both got hurt. That's just part of sports."
The Royals will take on the first-place White Sox without two key hitters in the lineup.
"You never want to see a play that takes out two of your All-Star players: one [Gordon] for the month and the other for the rest of the season," Royals manager Ned Yost said. "It happens, you have to deal with it and you've got to move on."
Moustakas did not play in the next three games at Minnesota and was checked out by team physicians upon returning to Kansas City for a seven-game homestand beginning Thursday against the Chicago White Sox.
Moustakas, a 2015 All-Star, was hitting .240 with seven home runs and 13 RBIs in 27 games. It is Moustakas' second trip to the disabled list in May after missing three weeks with a broken left thumb.
"I've never been on the DL before. I've played through some injuries throughout my career," he said. "Most of them I've been able to get through, playing through pain, playing through discomfort.
"With my thumb, I felt like I was able to play through that, but at the end of the day I wasn't able to hold my bat, so it stopped me from playing."