Positive associations have been found between executive function (EF) and language skills in young children. However, the relations between specific components of EF and language are unclear. This study examined these relations among young children in three Asian countries. A series of EF and language tasks was administered to 700 children (350 girls) aged from 3 to 6 years from urban and rural areas in Bangladesh (n = 232), China (n = 233), and India (n = 235). Overall EF was positively associated with oral language and literacy after controlling for age, socio-demographic variables, and country. Hierarchical linear regression analyses examined the associations of three EF components (working memory, shifting, and inhibitory control) with oral language and literacy. In all three contexts, inhibitory control was significantly associated with oral language; and working memory was significantly associated with literacy. Specific patterns of relations between EF components and language were observed across contexts. Future research may consider whether these findings can be generalized to different language systems.