Infantas was born in Córdoba in 1534, a descendant of Juan Fernández de Córdoba who had conveyed the two daughters, infantas (hence the surname), of Pedro I of Castile to safety after the Battle of Montiel in 1369. The family was still notable in Cordoba at the time of Fernando's birth and he enjoyed a privileged education, and later a patrimonio, or stipend, remitted to him in Rome from his family in Spain.

From 1572 - 1597 Infantas resided in Rome, voluntarily giving his services to a hospital for the poor. In 1577 Infantas came into conflict with Pope Gregory XIII and the composers Palestrina and Annibale Zoilo over the reversal of reforms in Gregorian chant, at one point causing his sponsor Philip II of Spain to instruct the Spanish ambassador in Spain to intercede with the Pope.

In 1584 Infantas took holy orders and served a small church on Rome's outskirts. He had returned to Spain by 1608 and presumably died around 1610.

From 1584 till his death Infantas was constantly involved in theological debate. In later life, he was embroiled in the regalist and Molinist controversies. His Treaty on Predestination (Paris, 1601), brought the charge of being an illuminist, if not a quietist, and the attention of the Spanish Inquisition. At the end of his life, overwhelmed by his theological enemies he was reduced to beggary and died in poverty.

Infantas' theological views may have influenced his preference, aside from the then standard Marian motets, for predominantly Biblical text settings in his publications. This is most notable in two almost unique settings of the Symbolum Apostolorum, a Credo according to the Apostle's Creed, not according to the ordinary of the mass. Infantas left no conventional mass setting. Michael Noone suggests that, although it is possible that Infantas may have been aware of a setting by the French composer Le Brung printed in 1540, it is equally likely that Infantas believed his settings to be unique. A third setting was visibly absent from the Pater Noster sequence in Book III, possibly as a result of criticism.