The 2015 winner has raced just twice since that victory and missed the King George VI Chase on Boxing Day.
"I'm afraid it's not going to happen, which is a real shame," said Bradstock, the wife of trainer Mark.
"When you have a horse like this you must not take any risks and there is no point going there half-baked."
She added: "He has just niggled the bone - he is still walking at the moment, but we must not take a risk as these niggling things can turn into fractures.
"We will not rush him and we will make sure he is fine before he comes back."
Bradstock said she hoped to see the 10-year-old race at the Punchestown Gold Cup in Ireland on 26 April but could not guarantee he would make the Bowl Chase at Aintree on 6 April.
Coneygree last raced after a year out with a hock injury at Haydock in November, impressing as runner-up to Cue Card.
"He ran a great race at Haydock, but he might have been feeling this coming on," said Bradstock.
"He has no miles on the clock and I'm hoping he can become a veteran record-breaker and a novice record-breaker.
"He is in very good nick, mentally, and is full of himself."
Former champion Coneygree will not run in the Cheltenham Gold Cup on 17 March due to a "niggling" injury, says assistant trainer Sara Bradstock.