The Rangers announced Darvish's injury 2 1/2 hours before he was scheduled to face the A's. Scott Feldman will start in Darvish's place.
The Rangers say Darvish felt stiffness on Tuesday morning. The club also says it is not known when Darvish will make his next start.
Darvish, who is 4-0 in his past five starts, is 16-9 with a 3.90 ERA. The Japanese rookie has 214 strikeouts, which ranks third in the AL.
The first-place Rangers entered Tuesday with a five-game lead over the Athletics.