A family spokesman said on Wednesday that Pointer had died at Santa Monica University of California, Los Angeles, Medical Centre on Tuesday.
He said that two sisters, Ruth and Anita, and two brothers, Aaron and Fritz, were at her side at centre in Santa Monica when she died.
Pointer had been hospitalised since late February. The type of cancer was not disclosed.
The four sisters grew up singing in the choir of an Oakland, California, church where their parents were ministers.
Bonnie and June formed a singing duo and began performing in clubs around the San Francisco Bay area.
Anita and Ruth later joined the group, which sang backup for artists such as Taj Mahal, Boz Scaggs and Elvin Bishop.
The sisters had hits in the 70s and 80s with Fire, Slow Hand and I'm So Excited.
Their self-titled debut album was released in 1973, and the song Yes We Can Can became their first hit.
They followed up with That's A Plenty, which featured an eclectic mix of musical styles ranging from jazz to country and pop.
They won a Grammy Award in 1974 for best country vocal performance by a group for the song Fairytale.
Bonnie Pointer left the group in 1977 for a solo career.
The Pointer Sisters recorded several more albums, including 1984's Break Out, which won two Grammys for Automatic and Jump (for My Love).
The album's other hit song, Neutron Dance, was prominently featured in the movie Beverly Hills Cop.
June recorded two solo albums, and later left the trio.
Anita and Ruth still perform under the group's name. Ruth's daughter, Issa Pointer, is the trio's newest member.