- Daughter of Tomás Velasco Saavedra (d. 1950) of Puebla and María Elena Fragoso Peón (d. 1998) of Acámbaro, Guanajuato.
- Sister of Susy Velasco.
- Puerto Rican-born director Fernando Cortés (husband of movie star Mapy Cortés) directed La India María's first seven movies. Rogelio A. González directed the eighth one. Gilberto Martínez Solares directed the next two. Velasco herself directed four and her son Iván Lipkies directed the final two.
- Her husband, Julián de Meriche, appeared in two of her India María movies: Tonta, tonta, pero no tanto (1972) and Pobre, pero honrada! (1973).
- Paternal grandmother of Iván Lipkies Barro.
- Occasionally she played other characters: a Spanish stage star in Ni Chana, ni Juana (1984), a Mexican presidential candidate in Las delicias del poder (1999), and a huapango dance teacher in Huapango (2004).
- A gifted singer-songwriter, she usually wrote and sang songs for her movies. She also recorded two albums as La India María: La mejor cantante de todas las grabadoras (1971) and De chile, de dulce y de manteca (1982).
- She co-starred with Ángel Garasa in two of her India María movies: Pobre, pero honrada! (1973) and Duro pero seguro (1978).
- She co-starred with Fernando Soler in two of her India María movies: Pobre, pero honrada! (1973) and La comadrita (1978).
- Armando Soto La Marina played her grandfather in two of her India María movies: Okey, Mister Pancho (1981) and El coyote emplumado (1983).
- Winner of the Mexican Theatre Critics Association's Celia Montalván Award for her stage show México canta y aguanta (1994).
- Winner of a 1989 Premio El Heraldo de México for her 35 years in show business.
- Winner of the 1987 Premio Taquilla de Oro ("Golden Box-Office Award") for being the most financially successful Mexican movie star of 1986.
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