The band said that McVie, 67, will be receiving cancer treatment during Fleetwood Mac's 14 scheduled tour dates in Australia and New Zealand in November and December.
"We are sorry to not be able to play these Australian and New Zealand dates," the band said in a statement on its Facebook page. "We hope our Australian and New Zealand fans as well as Fleetwood Mac fans everywhere will join us in wishing John and his family all the best.”
Fleetwood Mac's Lindsey Buckingham, Mick Fleetwood, Stevie Nicks and McVie started a world tour last April, and just recently finished their shows in Europe.
The band's moniker comes from the combination of Fleetwood and McVie's last names.
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