One in three children will be living in absolute poverty by 2030/31, according to new analysis published by the Scottish government.
It commissioned independent projections as part of work to draw up a poverty action plan.
Ministers said the figures reflected the damage caused by UK government welfare cuts.
Opposition parties said the SNP had to do more to tackle the "complex causes" of deprivation.
The Scottish government commissioned the research into child poverty levels as part of its Tackling Poverty Delivery plan, due to be published later this week.
The analysis, which takes into account tax and benefit changes announced by the UK and Scottish governments, suggested that the percentage of children living in relative poverty - which measures the gap between low and middle-income households - will increase from 23% in 2018/19 to 38% in 2030/31.
It found that absolute poverty - a measure of whether poorest households' incomes are keeping pace with inflation - will rise from 20% to 32%.
Meanwhile 16% of children will be in "persistent" poverty, up from 10%.
The key reason for the increases was cited as UK government cuts, including the benefit freeze and the two-child limit on tax credits.
Communities Secretary Angela Constance said: "This reveals the long-term damage of UK government welfare cuts and austerity, with alarming increases across every measure of child poverty.
"The UK government must urgently and drastically change course.
"If they won't, then they must deliver the necessary powers and financial levers to Scotland so we can do things differently and actually lift people out of poverty as opposed to only being able to mitigate the UK government's cuts."
Last November, MSPs passed a bill containing a series of targets for the reduction of child poverty in Scotland.
The Child Poverty (Scotland) Bill sets out four statutory goals which the government is expected to hit by 2030.
The Scottish Conservatives' equalities spokeswoman Annie Wells said: "These (latest) figures are deeply concerning, and they continue a trend we've seen over the past few years.
"They demonstrate the SNP's total inability to understand and address the complex cause of child poverty.
"We hope that the current ambitious child poverty targets can be met, but this makes clear that the SNP's current approach is simply not working."
Scottish Labour's Elaine Smith said ministers should reconsider her party's plans to use Holyrood's new powers to top-up child benefit.
"With one million people in Scotland living in poverty right now, we cannot afford to continue to tinker around the edges," she said.