Despite the high burden of Plasmodium vivax malaria in South Asian countries, the genetic diversity of circulating parasite populations is not well described. Determinants of antimalarial drug susceptibility for P. vivax in the region have not been characterised. Our genomic analysis of global P. vivax (n = 558) establishes South Asian isolates (n = 92) as a distinct subpopulation, which shares ancestry with some East African and South East Asian parasites. Signals of positive selection are linked to drug resistance-associated loci including pvkelch10, pvmrp1, pvdhfr and pvdhps, and two loci linked to P. vivax invasion of reticulocytes, pvrbp1a and pvrbp1b. Significant identity-by-descent was found in extended chromosome regions common to P. vivax from India and Ethiopia, including the pvdbp gene associated with Duffy blood group binding. Our investigation provides new understanding of global P. vivax population structure and genomic diversity, and genetic evidence of recent directional selection in this important human pathogen.