Velásquez, the fifth of six children, was born in Zulia State, Venezuela to a Venezuelan mestizo father and an Amerindian mother of the Wayuu people. Her parents were both teachers; her father also worked for UNESCO and as a result, she spent some of her childhood in Mexico and France. She attended San Vicente de Paul High School, graduating in 1987. After 3 years of college studies, Velásquez left for Milan, Italy, in pursuit of a modeling career.
In 2002, Velásquez founded the Wayúu Tayá Foundation, a non-profit organization dedicated to assisting the Wayúu, a Venezuelan indigenous group. In 2010, after the devastating Haiti earthquake, she had the Wayuú Tayá Foundation commission a special symbol of hope to raise money for the victims of the Haiti earthquake along with the slogan: Keep the “H” Close to Your Heart — Help Haiti Hope. She is fluent in English, French, Italian and Spanish.