Kouzmanoff was hitting .362 with two home runs and 10 RBIs in 13 games since replacing Beltre, who has been sidelined with a strained left quad muscle.
The Rangers have not made a move with outfielder Shin-Soo Choo, who is sidelined with a sprained left ankle, but he is not in the starting lineup on Friday against the Mariners. Michael Choice was in left field and batting leadoff for the third consecutive game.
The Rangers also lost pitcher Hector Noesi to the White Sox on a waiver claim. He was designated for assignment earlier this week.
T.R. Sullivan is a reporter for MLB.com. Read his blog, Postcards from Elysian Fields, and follow him on Twitter @Sullivan_Ranger. This story was not subject to the approval of Major League Baseball or its clubs.