Pinzon was born in the southern Spanish seaport town of Palos, to a family of Spanish shipowners. His brother, Vicente Yáñez Pinzon, commanded the Nina; his other brother, Francisco Pinzon, was the pilot (first mate) of the Pinta.

Martin Alonzo Pinzon often disobeyed the orders of Columbus during the voyage to the Americas (1492-1493). Contrary to Columbus' orders, he sailed off on his own while near Cuba, trying to make his own discoveries and find treasures (gold, silver, and spices). He returned to meet Columbus a few months later, when the fleet was to sail back to Spain. Upon his return, he found the Nina, but the Santa Maria had been wrecked. During the trip home, he once again left the fleet; he tried to race home to Spain in order to beat Columbus and become famous. Columbus reached Spain first.