The 79-year-old died peacefully in her sleep on Wednesday after a short illness, her family says.
Fleetwood Mac, whose name was inspired by the surnames of its founders - bassist John McVie and drummer Mick Fleetwood - formed in 1967 but had many members come and go over the years.
Born Christine Perfect in northwest England on July 12, 1943, she joined the band as a singer and pianist in 1970 after marrying John following a courtship of two weeks.
She ultimately left him to live with a lighting technician.
The British-American rock band's 1977 album Rumours, which sold more than 40 million copies and is one of the best-selling albums of all time, was recorded as the couple were divorcing.
McVie's family said she died peacefully in hospital.
"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," the statement said.
In a statement posted on Twitter, Fleetwood Mac said 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," the band said. "She will be so very missed.
As well as working with Fleetwood Mac, McVie also released three solo albums.
Eight of her songs appeared on the band’s 1988 Greatest Hits album.
In 1998, she was inducted into the Rock and Roll Hall of Fame as a member of Fleetwood Mac.
- Reuters and NZ Herald
