Rodriguez, regarded by many as the best all-around catcher in the majors, began the day batting .347 with 27 home runs and 83 RBIs.
Rodriguez was hurt when his thumb hit Mo Vaughn's bat on a swinging third strike as he threw to second base on a steal attempt by Kevin Stocker.
Stocker was called out by home plate umpire Gerry Davis on batter's interference.
Rodriguez was taken to a hospital for X-rays, which revealed the fracture. The Rangers said he would have surgery Tuesday.
"As soon as it happened, my thumb went numb. There was swelling and I knew it was broken and I'd be out for the season," he said.
The Rangers, the AL West champion the last two seasons, began the night 10 1/2 games behind division-leading Seattle.
Rodriguez, 28, played earlier this month in his ninth straight All-Star game. He has won eight consecutive Gold Glove awards, an AL record.
This year, he had thrown out 16 of 33 (48.5 percent) would-be basestealers. Last year, he caught 54.2 percent, the fifth straight season he led the AL in that category.
Rodriguez won the MVP last year when he hit .332 with an AL-record 35 home runs by a catcher. He had 113 RBIs and scored 116 runs.