Slowey (10-3) left his start Friday against Detroit after just three innings because of the injury. While trying to become baseball's first 11-game winner this season, the right-hander gave up six earned runs and five hits in three innings in an 11-9 loss.
He said on the team's Web site Saturday this is the first time this season he's experienced pain in his wrist and he didn't feel anything in his previous three-inning start June 27 against the St. Louis Cardinals.
"It was something that kind of affected how I held onto the ball, grip strength, etc.," he said. "It was just very, very uncomfortable."
Slowey is scheduled to undergo an MRI Monday.
Twins' Manager Ron Gardenhire said right-hander Anthony Swarzak will make Slowey's next scheduled start Thursday against the New York Yankees.