The horse, who won the Betfair Chase at Haydock Park and is ridden by Tizzard's son Joe, has a muscle injury.
Cue Card won the Ryanair Chase at last year's Cheltenham Festival and was set to step up to contest the Gold Cup.
The withdrawal is another blow for the meet as 2013 Champion Chase winner Sprinter Sacre will also be absent.
"Unfortunately, he has pulled muscles behind and he won't be running at the Cheltenham Festival," said Dorset-based Tizzard.
"We first noticed it last week. It was only a small thing then and it is only small now, but we cantered him this morning and he is still not right.
"He hasn't got any better and you can't be going to Cheltenham 90%. The horse has looked after me for the last four years and it is my turn to look after him."
Asked whether his stable star could be back in action at the Grand National meeting at Aintree in April, Tizzard said: "Hopefully, but we need to get him right first."
Eight-year-old Cue Card beat 2013's Gold Cup winner Bobs Worth in the Betfair Chase in November.