Enrique Enríquez (September 30, 1701 – April 25, 1756) was an Italian Roman Catholic cardinal.
Born in Campi Salentina, Puglia, he studied canon and civil law in the La Sapienza University, Rome, was later made governor of several towns in Italy until 1743, when he received the minor orders.
On December 16, 1743 he was elected titular archbishop of Nazianzo and sent Apostolic nuncio in Spain on January 8, 1744. Pope Benedict XIV created him cardinal priest in the consistory of November 26, 1753, with the title of Sant'Eusebio. As legate to Ravenna, he reestablished the independence of the Republic of San Marino, which his predecessor Cardinal Giulio Alberoni had suppressed.
Enriquez died in 1756 at Ravenna.