The Royals expect Moustakas to recover in time for Spring Training in 2017.
Moustakas injured his knee during a May 22 collision with teammate Alex Gordon while chasing a foul ball.
Young gets the nod Right-hander Chris Young will start on Sunday in place of right-hander Dillon Gee, who was optioned to Triple-A Omaha.
Young, who recently came off the disabled list (strained forearm), has pitched four scoreless innings since his return.
"He's got life on his fastball again," Yost said.
Medlen to Arizona Right-hander Kris Medlen, on the disabled list with a strained rotator cuff, continues his recovery and will have two more side sessions in Kansas City before being sent to the Royals' Spring Training site in Arizona for further rehab.
"He'll pitch live BPs [batting practice] and then we will evaluate him again," Yost said. "It's hard to get to do live BP on the road -- easier at home. So we'll send him down there."