Clara was born in Mantua on 1 July 1464, the eldest daughter of Federico I Gonzaga, Marquess of Mantua and Margaret of Bavaria (1 January 1442 - 14 October 1479).
Clara's paternal grandparents were Ludovico III Gonzaga and Barbara of Brandenburg; and her maternal grandparents were Albert III, Duke of Bavaria and Anna of Brunswick-Grubenhagen-Einbeck, daughter of Duke Erich I of Brunswick-Salzderhelden and Elisabeth of Brunswick-Göttingen.