Meanwhile, more than one in four Scots parents on low incomes say they are arguing more because of stress about money.
The results were published by Save the Children, which carried out two major surveys to obtain the data.
They reinforce figures published separately by Citizens Advice Scotland (CAS), which claimed thousands of Scots were having to rely on food parcels. As The Herald reported yesterday, CAS said 2200 of its clients now relied on food banks, a figure that has doubled in two years.
The new findings came from an online survey of 1504 schoolchildren aged 8-16 across the UK, and a survey of 5000 parents on low, middle and high incomes, of whom 1527 were in Scotland.
Save the Children found more than 40% of parents in Scotland on low incomes have less than £30 per week to spend on food for the entire family, compared to a national average of £76 per week, and around three-fifths of the poorest families in Scotland have had to cut the amount they spend on food in the last year.
Almost 40% of parents in the worst-off families are stressed and constantly worry about how to make ends meet. One in seven children in these families regularly do not get enough to eat.
The charity also says almost half of the poorest families are short of money every week and nearly 30% have nothing left to cut back on.
One in six children in the most impoverished homes often feel run down or unwell because of poor diet and living conditions.
Parents are arguing more and at least 20% say they are increasingly likely to snap at their children because of money worries.
Save the Children said witnessing the financial worries of their parents could place an impossible burden on children. One 11-year-old, identified only as Duncan, told researchers: "My mum makes sacrifices so that I can do the hobbies I want to do to keep me off the streets. She cuts back on buying herself new shoes and clothes."
Sharon, a single parent from Glasgow, said: "When you're on a low income, every single penny comes into it, even small things that others take for granted. I try not to talk about money too much with my kids but obviously they're very aware I'm on my own and I struggle for money."
Sara, a mother living in poverty in Edinburgh, said: "Some of the hardest things to pay for are everyday stuff like washing-up liquid and toilet roll and prices seem to be getting higher. I'm always trying to explain to my kids that I'm skint and I'm not being nasty to have to say no all the time. It's really hard."
Douglas Hamilton, head of Save the Children in Scotland, said: "Children should not be bearing the brunt of the recession. Poverty is tearing families apart, with parents buckling under the pressure of mounting bills and children seeing their parents argue more about money. It's inexcusable that this is happening in Scotland in 2012.
"Given nearly half of children living in poverty in Scotland have at least one parent in work, it is truly appalling those parents can't earn enough to give themselves and their kids a decent life. The Scottish Government must do more by supporting parents into work, make work pay, provide extra childcare and protect the poorest and most disadvantaged from further cuts."