Brett left Tuesday's 1-0 loss to the Red Sox after getting picked off by Wade Miley at first base in the bottom of the third.
To take Brett's place, the Rays selected infielder Jake Elmore from Triple-A Durham. To make room for Elmore on the 40-man roster, Jeff Beliveau was transferred to the 60-day disabled list after announcing that the left-hander would have shoulder surgery on Thursday to repair a torn left labrum.
"[Elmore] provides a ton of versatility," Cash said. "He's played well down there. He's been having really good at-bats. It was nice to see him during Spring Training. He was the guy that we carried on every single trip simply because if he wasn't starting, he covered us at any position -- and that's a luxury to have in the dugout."
Elmore, 27, signed with the Rays as a free agent on Feb. 9. He has a .221 career average with two home runs and 13 RBIs in 87 Major League games with the D-backs, Astros and Reds. He is hitting .333 with five RBIs for the Bulls this season.
Brett's addition moved the number of Rays currently on the DL to 11 players, the most in the Major Leagues and setting a new club record for the most at one time.
Bill Chastain is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.