The singer was one of the founding members of R&B group the Pointer Sisters, whose hits included "I'm So Excited," and "Jump" and whose fame was at its height in the 1970s and 1980s.
Pointer died on Saturday at her home in Los Angeles where she was surrounded by family, her publicist Roger Neal said.
"Sad to report my client, Grammy Winner Anita Pointer of the Pointer Sisters, has passed away after a heroic battle with cancer," Roger Neal said on Instagram.
The group's official website listed the group's achievements and carried a statement from the family.
What reaction has there been to Pointer's death?
"While we are deeply saddened by the loss of Anita, we are comforted in knowing she is now with her daughter, Jada, and her sisters June & Bonnie and at peace," the statement said.
"Heaven is a more loving beautiful place with Anita there."
The group's debut Grammy-winning hit in 1974 was "Fairytale," which crossed over from the country charts to the pop charts.
Anita spoke of how excited she was when Elvis recorded the song and started to sing it at concerts until his death in 1977.
Who are The Pointer Sisters?
The Pointer Sisters made their movie debut singing in the feature film "Car Wash," starring Richard Pryor.
A remixed version of their track "I'm So Excited" hit new highs for the group in the music charts, followed by "Neutron Dance," which featured in the hit film "Beverly Hills Cop."
However, it was the "Breakout" album that really gave the Pointer Sisters their biggest slice of fame, going triple platinum with hits like "Jump” and "Automatic."
Anita founded the group in Oakland, California, with sisters June and Bonnie, who were later joined by younger sibling Ruth.
The Pointer Sisters won three Grammy Awards in all and received a star on the prestigious Hollywood Walk of Fame in 1994.