Sledge was discovered dead at her home in Phoenix, Arizona, by a friend on Friday.
The band’s publicist, Biff Warren, said a cause of death has not been established and that Sledge had not been ill.
The family said in a statement: “On yesterday, numbness fell upon our family. We welcome your prayers as we weep the loss of our sister, mother, aunt, niece and cousin.”
Sledge and her sisters Debbie, Kim and Kathy formed Sister Sledge in 1971, and had their breakout success with the album We Are Family in 1979.
The title track was an infectious song that celebrated their familial connection with the refrain: “We are family, I got all my sisters with me.”
The song, which sold more than a million copies, was nominated for a Grammy and became an anthem of unity and women’s empowerment.
Other hits on the album included Lost In Music, Thinking Of You and He’s The Greatest Dancer.
The songs were co-written and produced by Chic star Nile Rodgers, who paid tribute to Joni.
He tweeted his condolences to the family and added: “We did something pretty amazing together.”
— Nile Rodgers (@nilerodgers) March 12, 2017
La Toya Jackson also paid tribute on Twitter while TV Star Ru Paul tweeted “Sister Sledge Forever”.
Although Sister Sledge reached their peak in the US in the late 1970s their biggest UK hit came in 1985.
Frankie stayed at number one for four weeks and was one of the biggest selling songs of the year.
When sister Kathy left for a solo career in 1989, the remaining members continued to perform and record.
Several of their songs were re-released in the UK in the early 1990s and became hits all over again and, in 2015, they performed for Pope Francis.
They last performed together in concert in October.
Joni Sledge is survived by a son.