Social workers warned the parents they have only three months to help three of their six children shed the pounds.
They want to see an improvement by June in the 12-year-old boy, who weighs 16 stone, and two of his sisters, aged 11 and three, who weigh 12st and 4st respectively.
The family, from Dundee, have been ordered to send their children to dance and football lessons to help them lose weight.
Another couple from the city are facing the same fate over concerns their only child is obese.
The development highlights Scotland's childhood obesity crisis, which has already forced some as young as 13 to seek NHS weight-loss surgery. Only the United States has more overweight children, underlining fears that our current generation of youngsters may not outlive their parents.
But politicians and health experts have described the intervention of social workers as "deeply worrying" and questioned their powers to break up families.
The family, who have not been named to protect the children, said their slimming deadline was set at a meeting with child protection officers, in which they were warned all six youngsters would be taken away.
The 39-year-old mother, who weighs 23 stone, said: "This is every family's worst nightmare. We have been told they are going to take them from us unless three of them lose weight.
"I just can't stop crying at the thought I could lose my beautiful children for ever."
She went on: "They keep making an issue about the kids' weight. Social workers have even tried to tell us our baby is fat.
"I don't even own a deep-fat fryer. All my food is home-cooked and the kids are not fed junk food at all. I feel we are being victimised. Children can carry a bit of puppy fat, but they tend to lose it as they get older. Ours are not being given that chance."
Mary Scanlon, the Scottish Conservatives' health spokeswoman, said: "To punish the family by taking the children into care because of their weight is not positive or helpful – it is deeply worrying.
"The decision to take children into care has to be a last resort. Splitting up a family should be the very last consideration where the future health of the child is at great risk."
Dr Colin Waine, of the National Obesity Forum, said: "This has to be a last resort. We must understand the health dangers associated with obesity, but the approach I favour is regular monitoring of children's weight from birth to avoid drastic action like this."
Dundee City Council said: "We are not able to comment on individual child protection issues."
A Scottish Government spokesman said: "Obesity is an increasing problem and poses a very serious threat to our nation's health."
COUNTRY'S ALREADY-WORRYING OBESITY RATES ON THE RISE
SCOTLAND is the second fattest nation on Earth, with only the US weighing in heavier.
Figures published last year found that one in six boys and one in seven girls in Scotland are obese. For adults the rate is worse, at one man in four and one woman in five.
A report by the Scottish Public Health Observatory in September also found obesity was not limited to deprived inner cities. More than 70 per cent of men and 65 per cent of women in Orkney, Shetland and the Western Isles are either overweight or obese – the highest rate in the country.
Almost 500,000 cases of high blood pressure can be attributed to obesity, as well as more than 5,000 strokes a year and almost 30 per cent of all colon cancer cases.
The cost of treating these obesity-related diseases was last estimated six years ago, at 171 million.
In 2003, the Scottish Health Survey showed that obesity rates had increased significantly in recent years, with 22 per cent of men deemed obese compared with 16 per cent in 1995, and 24 per cent of women obese, up from 17 per cent in 1995.
Overall, 64 per cent of men and 57 per cent of women were either overweight or obese in the 2003 figures.