Íñigo was born in Guadalajara, Kingdom of Castile, and was educated along with his brother, Diego Hurtado de Mendoza y Quiñones (who would later become a cardinal), in the palatial house of his grandfather.

He would also receive instruction in political and military matters from his father, the ambassador to Pope Pius II in the council of Mantua and from his uncle, the powerful cardinal Pedro González de Mendoza.

Succeeding his father in 1479 as Conde de Tendilla, he entered the Royal Court at Toledo in 1480 to show his loyalty to the Catholic Monarchs and offered his services for the ongoing conquest of Granada.

[5] During his tenure, he accomplished a very ambitious agenda which included: pushing for a peace treaty between the Pope and the Kingdom of Naples, renewing the papal bull favoring the Crusade of 1482, reforming the church, and giving the power to appoint bishops to the king.

During his tenure as governor, Conde Íñigo subdued the first Moorish uprising in Granada (1500–1502), which was brought about by the forced mass conversions enacted by Cardinal Francisco Jiménez de Cisneros.