The Twins were hoping Slowey would be able to throw on Sunday to test how the wrist reacted to a cortisone shot. But manager Ron Gardenhire said the pitcher was not able to throw. Slowey will instead try to throw on Wednesday.
Rookie Anthony Swarzak will make Slowey's next start, which was slated for July 21 at Oakland.
Slowey was placed on the disabled list on July 4. His 10 victories this season are tied for second most in the American League.
Gardenhire said the Twins will wait until Slowey throws on Wednesday before deciding about any further treatment for the injury.