New figures from the Campaign to End Child Poverty show "unacceptably high levels of child poverty" in 29 of 32 local authority areas.
Some of the bleakest concern Glasgow, where 14 of 21 wards have more than 30% of children living in poverty.
In Glasgow's Springburn 51% of children live in poverty, and in the Calton area the level is 49%. In Edinburgh the highest level is 35%, recorded in Sighthill and Gorgie.
The Scottish Government said the figures were a scandal and that UK Government welfare changes would further damage the "social fabric of Scotland."
John Dickie, speaking on behalf of Scottish members of the Campaign to End Child Poverty, said the figures would get worse in the coming years.
He said there was a "hidden picture that is far more sinister as the ripping away of [benefits and tax credit] support is forecast to drive tens of thousands of children into poverty across Scotland in the coming years".
He added: "These projections are a sad indictment for our next generation. Rising child poverty means more children growing up in cold or damp homes, more children missing out at school and more children seeing their health undermined.
"The huge disparities that exist across the country have become more entrenched, and now risk becoming an enduring reality."
The Scottish Government estimates at least 65,000 more children will be living in poverty in Scotland by 2020.
Glasgow City's average of 33% of children living in poverty is the highest in Scotland, followed by Dundee (26%) and West Dunbartonshire and North Ayrshire (25%).
A Scottish Government spokesman said: "It is nothing short of a scandal that any child should live in poverty in a resource-rich country like Scotland, and this report simply underlines the urgent need for Scotland to have the economic powers required to tackle poverty.
"The fact that this report also predicts a worsening picture of child poverty is a stark warning of the continued damage which UK Government welfare cuts are poised to inflict to the social fabric of Scotland."
Scottish members of the Campaign to End Child Poverty include Action for Children Scotland, Barnardo's Scotland, the Child Poverty Action Group in Scotland, Children 1st, the Church of Scotland, One Parent Families Scotland, Poverty Alliance and Save the Children.
A spokesman for the Department of Work and Pensions said: "The previous Government failed to meet their target to halve child poverty by 2010, and far too many children were left behind.
"This Government remains committed to eradicating child poverty, but we want to take a new approach by tackling the root causes including worklessness, educational failure and family breakdown.
"Our welfare reforms will improve the lives of some of the poorest families in our communities, with the Universal Credit simplifying the complex myriad of benefits and making three million people better off".
Scottish Labour's Drew Smith MSP said progress to reduce child poverty had stalled under the present SNP administration at Holyrood.
He added: "I believe the Scottish Parliament can and should make a difference. More can – and should – be done.
"We need to build new homes, get more people into college, and into work, target help at those who need it most and support the living wage to lift people out of poverty.
"Tackling poverty could be the absolute priority for Scottish governments. But with the SNP, everything takes second place to the constitution."