María Elena Velasco was born in Puebla, to Tomás Velasco, a railway mechanic, and María Elena Fragoso. She had three siblings, Gloria, Tomás and Susana. After the death of Tomás Velasco, the family moved to Mexico City, where she worked as a dancer at the Teatro Tívoli. Later, she became one of the showgirls of the Teatro Blanquita, where she also participated in sketches starring comedians such as José “El Ojón” Jasso and Óscar Ortiz de Pinedo, among others. In 1962, her popularity at the Teatro Blanquita attracted the attention of producer Miguel Morayta, who cast her in her first film role in the drama Los derechos de los hijos (1963), starring Elvira Quintana and Carlos Agostí. Juan Bustillo Oro gave her the small part of Petra, a maid, in México de mis recuerdos (1963). In 1964, she began to include comedic material to her appearances in sketches and, in the meantime, played servants in television programs. She soon developed a comedy character named Elena María, a rural Mexican woman. Her breakthrough came when director Fernando Cortés recommended her to portray an indigenous woman named “María” in one of Mantequilla’s sketches. The character was dressed in traditional garb consisting of traditionally braided and ribboned hair and colorful native-type blouses and skirts. In an effort to make her portrayal more authentic, she observed the gestures and mannerisms of indigenous women; her own mother made dresses for the character. She later appeared in the western El bastardo (1968), where she was credited for the first time as “María Elena Velasco ‘La India María'”. In 1969, Velasco appeared as La India María in a comic segment of the weekly program Siempre en domingo, hosted by Raúl Velasco. The segment quickly became a hit and she starred in other successful television programs. Her first La India María vehicle, Tonta, tonta, pero no tanto (1972), was directed by Fernando Cortés; in total, Cortés directed eight La India María films until his death in 1979. The enormous success of the film spawned a series of low-budget comedies that became a mainstay in Mexican movie theaters. Velasco won a Silver Goddess Award for Best Comedic Performance for ¡El que no corre… vuela! (1982). She made her directorial debut in El coyote emplumado (1983). She also starred the television series Ay María, qué puntería (1998).

In the early 1960s, Velasco met Russian-born Mexican film actor and choreographer Julián de Meriche (born Vladimir Lipkies Chazan) at the Teatro Blanquita. They married and had three children, producer-director Iván Lipkies, writer-actress Goretti Lipkies, and writer-producer Ivette Lipkies. She later said: “My husband was worth gold, I will not lie and say he was the perfect man, but he was the love of my life.” Her death was announced over Twitter by the Instituto Mexicano de Cinematografía on 1 May 2015; the cause of death was not made public, but it was known that she had been suffering from stomach cancer.