- Daughter of Tomás Velasco Saavedra (d. 1950) of Puebla and María Elena Fragoso Peón (d. 1998) of Acámbaro, Guanajuato.
- 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).
- 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 Neither Chana, Neither Juana (1985), a Mexican presidential candidate in Las delicias del poder (1999), and a huapango dance teacher in Huapango (2004).
- She co-starred with Ángel Garasa in two of her India María movies: Pobre, pero honrada! (1973) and Hard but Sure (1978).
- She co-starred with Fernando Soler in two of her India María movies: Pobre, pero honrada! (1973) and The Little Midwife (1978).
- Armando Soto La Marina played her grandfather in two of her India María movies: Okey, Mister Pancho (1981) and The Feathered Coyote (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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