We study subfields of large fields which are generated by infinite existentially definable subsets. We say that such subfields are existentially generated. Let L be a large field of characteristic exponent p, and let E⊆ L be an infinite existentially generated subfield. We show that E contains L (p n), the p n-th powers in L, for some n< ω. This generalises a result of Fehm from [4], which shows E= L, under the assumption that L is perfect. Our method is to first study existentially generated subfields of henselian fields. Since L is existentially closed in the henselian field L ((t)), our result follows.