Coltrane died Friday of respiratory failure at West Hills Hospital and Medical Center, said her sister, Marilyn McLeod.
For nearly 40 years, Coltrane managed the archive and estate of her husband, a pivotal figure in the history of jazz. He died of liver disease in 1967 at age 40.
A pianist and organist, Alice Coltrane was noted for her astral compositions and for bringing the harp onto the jazz bandstand.
Born Alice McLeod in Detroit on Aug. 27, 1937, she began learning classical piano at age 7. She studied jazz piano briefly in Paris before moving to New York, where she met her future husband in 1963.
At that time, she was playing with bandleader Terry Gibbs, who has often taken credit for introducing the two.
John Coltrane "saw something in her that was beautiful," Gibbs told the Los Angeles Times.
She left Gibbs' band to marry Coltrane and began performing with his band in the mid-1960s. She played tour dates with Coltrane's group in San Francisco, New York and Tokyo.
"John not only taught me how to explore but to play thoroughly and completely," Alice Coltrane said in comments published in "The Black Giants."
After his death, she devoted herself to raising their children but continued to play.
Early albums under her name, including "A Monastic Trio" and "Ptah, the El Daoud," received critical praise.
Her last recording, "Translinear Light," came in 2004. Her last performances came in an abbreviated tour last fall with her saxophonist son, Ravi.
Coltrane, a convert to Hinduism, was also a significant spiritual leader and founded the Vedantic Center, a spiritual commune now located in Agoura Hills.