During the broadcast of a June 18 game against the San Diego Padres, Barnett became nonsensical, saying, "the go-ahead run is at fifth on what (Rangers relief pitcher Mike) Adams is insisting on calling a botched robbery."
The team initially blamed the episode on a migraine, but Barnett was pulled off two subsequent telecasts and has not appeared since.
"Effective immediately, for health reasons I will be taking an indefinite leave of absence from my broadcasting duties that I expect to last for the remainder of the season," the announcer said in a statement. "I would ask that you please respect the privacy of me and my family during this time."
Steve Busby will continue to take Barnett's place in the booth, the team said.