Rios suffered a non-displaced fracture of the fifth metacarpal when the 12-year veteran was hit on the hand by a pitch from Minnesota's J.R. Graham.
Yost said Rios, who has yet to test the hand, will begin strengthening exercises later this week. The Royals manager is unsure if Rios will need a minor league rehabilitation assignment.
"It would probably be beneficial to get some at-bats, but we'll see. I don't know yet," Yost said.
Rios, 34, is batting .321 with a home run and eight RBIs this season for the defending AL champion Royals.
In other injury news, closer Greg Holland (strained pectoral muscle) was activated off the DL after Tuesday's game.
"He's fine and he's ready to go," Yost said.
Shortstop Alcides Escobar -- who suffered a concussion and is eligible to return Thursday -- is still waiting to be cleared by MLB doctors.
"He still has to clear tests by the league," Yost said. "The fogginess in his eyes is gone and he's doing a lot better. But it's not up to us."
The Associated Press contributed to this report.