The great ethnolinguistic diversity found today in mainland Southeast Asia (MSEA) reflects multiple migration waves of people in the past. Maritime trading between MSEA and India was established at the latest 300 BCE, and the formation of early states in Southeast Asia during the first millennium CE was strongly influenced by Indian culture, a cultural influence that is still prominent today. Several ancient Indian-influenced states were located in present-day Thailand, and various populations in the country are likely to be descendants of people from those states. To systematically explore Indian genetic heritage in MSEA populations, we generated genome-wide SNP data (using the Affymetrix Human Origins array) for 119 present-day individuals belonging to 10 ethnic groups from Thailand and co-analyzed them with published data using PCA, ADMIXTURE, and methods relying on f-statistics and on autosomal haplotypes. We found low levels of South Asian admixture in various MSEA populations for whom there is evidence of historical connections with the ancient Indian-influenced states but failed to find this genetic component in present-day hunter-gatherer groups and relatively isolated groups from the highlands of Northern Thailand. The results suggest that migration of Indian populations to MSEA may have been responsible for the spread of Indian culture in the region. Our results also support close genetic affinity between Kra-Dai-speaking (also known as Tai-Kadai) and Austronesian-speaking populations, which fits a linguistic hypothesis suggesting cladality of the two language families.