Born into a family of Conversos at Cuenca, Gómez entered the Spanish Army, where he obtained a Captaincy.
He adopted the name Antonio Enríquez Gómez, and became major-domo to King Louis XIII of France, to whom he dedicated Luis dado de Dios 4 Anna (Paris, 1645).
The Academias morales de las Musas, consisting of four plays (including A lo que obliga el honor, which recalls Calderón's Médico de su honra) was published at Bordeaux in 1642; La torre de Babilonia, containing the two parts of Fernán Mendez Pinto, appeared at Rouen in 1647; and in the preface to his poem, Sansón Nazareno (Rouen, 1656), Enríquez Gómez gives the titles of sixteen other plays issued, as he alleges, at Seville.
According to the Encyclopædia Britannica Eleventh Edition, "[h]is dramatic works, though effective on the stage, are disfigured by extravagant incidents and preciosity of diction.
Enríquez Gómez is best represented by El siglo pitagórico y vida de don Gregorio Guadana (Rouen, 1644), a striking picaresque novel in prose and verse which is still reprinted."