From Proto-Italic *genā, from Proto-Indo-European *ǵénu-, *ǵénus (“chin, jaw, cheek”). The declension was most likely changed to avoid confusion with genus.
Cognates include Ancient Greek γένυς (génus), Sanskrit हनु (hánu), Persian چانه (čâne), Tocharian A śanweṃ, Old Armenian ծնաւտ (cnawt), Lithuanian žandas, Welsh gen, and Old English ċinn (English chin).