Darvish gave up a leadoff single to Alcides Escobar before retiring the next three batters he faced. He threw 10 of 12 pitches for strikes before leaving for precautionary reasons.
A Rangers spokesman said he would be reevaluated Friday.
An All-Star each of his first three seasons, Darvish was 10-7 with a 3.06 ERA last year before missing most of the final two months with elbow inflammation. He also missed the end of spring training and the start of last season with neck stiffness.