She was 52.
Marlene Palmer, group's tour publicist, said Rankin's sister confirmed the death.
Rankin and her four siblings — John Morris, Jimmy, Cookie and Heather — formed the group more than 20 years ago and are credited with taking Cape Breton Celtic music to the mainstream.
In a statement provided by Palmer, Heather Rankin said her sister fought "a very long and courageous battle with grace and dignity and was an inspiration."
"Throughout her struggle with cancer she never ceased to show her concern for her friends and family," she said.
"Right up until her last hours of life she was still expressing concern for others. She worried for all of her family and friends, a beautiful lady indeed."
Heather Rankin described her sister as generous and kind hearted.
"She was a little bit older and she took on the role of protector of the younger members of her clan," she said.
"She was a very bright lady and a strong leader and I often looked to her for guidance and I will have a very large void in my life now that she is gone."
Members of Canada's music community were mourning Raylene Rankin's death on Sunday.
Fellow Cape Breton singer Rita MacNeil said she was devastated when she heard the news.
"I've known Raylene a long time. We have lost a great musician and a wonderful person," MacNeil said in a statement. "It's a lasting legacy. An inspiration to all women."
Singer Anne Murray added that Rankin will "live on through her music."
"It is a sad loss of a fine talent from a family who has endured so much tragedy already," she said in a statement.
In 2000, John Morris Rankin died when his truck plunged into the icy Gulf of St. Lawrence near Margaree Harbour, N.S. He was 40.
Federal Heritage Minister James Moore offered his condolences to Raylene Rankin's family and friends on Sunday.
"Her musical talent charmed the nation," he said in a statement which highlighted the many Canadian music awards won by The Rankin Family.
Father Angus Morris of St. Mary's Parish in Mabou, N.S., said Rankin is survived by her husband Colin Anderson and her son Alexander.
Rankin grew up in the close-knit community of Mabou with her mother Kathleen, her father Alexander and 12 siblings, The Rankin Family website said.
The family band first formed under the name The Rankins and won a host of awards over a 10 years period, the website said.
In 1999, the group went their separate ways, with many members pursuing solo careers, it said. But in 2007, the four siblings reunited to form The Rankin Family.
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