Well, it seems that its origin may be quite similar to the origin of other expressions such as ni mu or ni pío, with the same meaning and coming from onomatopoeias of animal sounds. Searching the word ñe in the RAE's Fichero general, one of the files found references the Glosario lexicográfico del Atlas lingüístico-etnográfico de Colombia, from authors Montes, Figueroa, Mora and Lozano, published in 1984, which says the following:
ñe, onomatopeya de la voz del toro.
Translated: ñe is the onomatopoeia of the sound of a bull in Colombia.
Given that Colombia and Venezuela are neighbor countries, it wouldn't be strange that that onomatopoeia is also known in the latter, hence people would just use it in place of mu, the onomatopoia of the sound of a cow.