The more than 1.5 billion people who live in South Asia are correctly viewed not as a single large population but as many small endogamous groups. We assembled genome-wide data from over 2,800 individuals from over 260 distinct South Asian groups. We identified 81 unique groups, 14 of which had estimated census sizes of more than 1 million, that descend from founder events more extreme than those in Ashkenazi Jews and Finns, both of which have high rates of recessive disease due to founder events. We identified multiple examples of recessive diseases in South Asia that are the result of such founder events. This study highlights an underappreciated opportunity for decreasing disease burden among South Asians through discovery of and testing for recessive disease-associated genes.