Rodrigo Díaz de Vivar Gómez de Sandoval y Mendoza (4 April 1614 – 14 January 1657) was a Spanish noble of the House of Mendoza and the 7th Duke of the Infantado, serving in this office from 1633 until his death in 1657.
The Dukedom of the Infantado had been in the hands of the Mendoza family since the very first duke, Diego Hurtado de Mendoza y Figueroa. The Mendoza family rose to power when it merged with the House of Lasso de la Vega through the marriage of Leonor Lasso de la Vega, the last direct member of that line, and Admiral Diego Hurtado de Mendoza, the admiral of Castile. He inherited the title from his grandmother, Ana de Mendoza y Enríquez de Cabrera.
He was the son of Diego Gómez de Sandoval y Rojas, 5th Duke of Lerma and Luisa de Mendoza, daughter of Ana de Mendoza y Enríquez de Cabrera, 6th Duchess of the Infantado. He became 7th Duke of the Infantado, when his grandmother died in 1633.
Rodrigo actively fought in the Portuguese Restoration War as a member of Philip IV of Spain's staff. He also participated in putting down the Catalan Revolt and in the Siege of Lérida. He was later named the Spanish ambassador to Rome, Governor of Milán, and Viceroy of Sicily.
He died in 1657 without leaving any heirs. As such, the title of Duke of the Infantado passed on to his sister, the Duchess of Pastrana, Catalina Gómez de Sandoval y Mendoza which united the two houses, Infantado and Pastrana, and increased the power of the family.
Rodrigo married in 1630 with María de Silva y Guzmán, the daughter of Ruy III Gómez de Silva y Mendoza de la Cerda, the 3rd Duke of Pastrana. The couple never conceived any children.