Galindo was awarded the following prizes and honours: Honorary Officer of the Order of the British Empire, Polish award for Cultural Merit, Order of the Star of Yugoslavia, Mariano Azuela Prize, the Bellas Artes Literature Prize, the Xavier Villarrutia Prize and the José Fuentes Mares Prize. He was elected to the Mexican Academy of the Language in 1975 and to the Spanish Royal Academy the following year. In 2006, the University of Veracruz and its International University Book Festival inaugurated an annual prize for first novels by Latin American writers, called the Premio Latinoamericano de Primera Novela Sergio Galindo. His works have been translated into English, French, Polish, German and Italian.