The British-American rock band, founded in London in 1967, sold more than 100 million records worldwide, making them one of the most successful groups ever.
Their best-known songs include Dreams, Go Your Own Way and Everywhere.
A statement from her family said: "It is with a heavy heart we are informing you of Christine's death. She passed away peacefully at hospital this morning, Wednesday, November 30th 2022, following a short illness.
"She was in the company of her family. We kindly ask that you respect the family's privacy at this extremely painful time and we would like everyone to keep Christine in their hearts and remember the life of an incredible human being, and revered musician who was loved universally."
Despite its tumultuous history, Fleetwood Mac became one of the best-known rock bands of the 1970s and '80s, comprising Mick Fleetwood, Christine and John McVie, as well as Lindsey Buckingham and Stevie Nicks.
Perhaps their best known album Rumours, released in 1977, became one of the best-selling albums ever and included hits such as Second Hand News and You Make Loving Fun.
As well as several multi-platinum tracks, the record sold more than 40 million copies worldwide.
A statement from the band said on Twitter: "There are no words to describe our sadness at the passing of Christine McVie. She was truly one-of-a-kind, special and talented beyond measure.
"She was the best musician anyone could have in their band and the best friend anyone could have in their life.
"We were so lucky to have a life with her. Individually and together, we cherished Christine deeply and are thankful for the amazing memories we have. She will be so very missed."
Singer-songwriter and keyboardist McVie penned Songbird, one of the band's most famous tracks, as well as You Make Loving Fun, Oh Daddy and Little Lies.
In 1970, the British-born McVie released her first solo album, Christine Perfect, after her maiden name. In an interview this year, she told Uncut magazine: "There's maybe a couple of good songs on it."
It took McVie another 14 years to release a follow-up solo album - titled Christine McVie - before releasing another album In The Meantime in 2004.
In June this year, the singer-songwriter released another album titled Songbird, a collection of songs drawn from two of her previous solo albums.
McVie was among the eight members of the band who were inducted into the Rock & Roll Hall of Fame in 1998.
In 2017, she appeared on BBC Radio 4's Desert Island Discs, revealing that she had retreated from the world and developed agoraphobia after she quit the band and moved from California to Kent, England.
McVie's death comes two years after Fleetwood Mac co-founder Peter Green died at the age of 73.
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