The Royals were already thin in the outfield after placing Lorenzo Cain on the disabled list with a strained groined earlier in the week.
Kansas City made the moves before Friday night's game against Minnesota.
Manager Ned Yost said he expects Dyson to return Monday in Cleveland.
Paredes was claimed off waivers from Baltimore in February, and was hitting .319 at Omaha. Yost views him as capable of playing second base, third base and any of the outfield spots.
In other injury news, Royals left-hander Bruce Chen said he's ready to pitch against the Twins on Saturday. He had his regular turn pushed back from Thursday because of a sore back.