Smith has been a starter in the minors, but Royals manager Ned Yost said he would provide protection as a long man out of the bullpen Tuesday night against the New York Yankees.
Getz has a bruised left ribcage and strained cartilage between his ribs, making it uncomfortable to breathe at times. He is batting .277 with no homers, eight RBIs and six stolen bases.
"It's just unfortunate. I felt pretty good at the plate and was helping the team," Getz said. "It's a good thing it's not too serious of an injury."
Yost said he would be very surprised if Getz is out any longer than 15 days.
Getz aggravated the injury Monday night when he slid into second base and was tagged out trying to stretch a single. He left the game an inning later.
Tests showed no fractures or tears, an encouraging sign. Getz originally got hurt in a collision at first base with Baltimore's Chris Davis last week.
"He won that battle, unfortunately," Getz said.
To make room for Smith on the 40-man roster, the Royals transferred right-hander Blake Wood from the 15-day disabled list to the 60-day DL.