Tigernut tubers (Cyperus esculentus) are used for the production of vegetable milk, commonly known as “Horchata de chufa” in Spain. The presence of starch in the tuber limits the yield of the milk, since this carbohydrate gelatinizes during the pasteurization of the milk and leads to the considerable solidification of this drink. The present work aims to improve the yields and extraction practice of the milk by an in situ hydrolysis of starch, using exogenous amylases of industrial or vegetable origin. The obtained results show that sprouting improves the extraction yields of tigernut milk, which goes from 50% to about 70%. This improvement in milk yield corresponds to a hydrolysis of about 35% of the starch in the tuber. The use of exogenous amylases leads to starch hydrolysis rates of 45% and 70%, respectively, for amylolytic extracts from sprouted tigernut tubers and amylase, with the corollary of a natural increase in the sweetness of milk. This technical approach makes it possible to produce a naturally sweetened tigernut milk which easily lends itself to pasteurization without a significant increase in viscosity.