Scottish Government statistics for 2012-13 show 16% were classed as living in relative poverty - where their household income is less than 60% of the average.
But when housing costs were factored in that rose to 19% of the population - with 1,000,000 people facing financial difficulties after paying for their accommodation.
The number of children living in poverty also rose last year, along with the total of both working age adults and pensioners in this position.
Deputy First Minister Nicola Sturgeon said the statistics show independence is "vital" for Scotland to tackle the problem.
"Scotland is one of the richest counties in the world and there is no reason for children to be living in poverty in our society," she said.
"The fact is that the reduction in poverty seen in recent years is now being reversed. Westminster welfare reforms, such as the reduction in in-work tax credits, are reducing incomes for some of our poorest households."
A total of 180,000 children in Scotland were living in relative poverty in 2012-13, an increase of 30,000 from the previous year.
This means almost one in five youngsters (19%) were affected, up from 15% in 2011-12.
Meanwhile, 480,000 people of working age were classed as living in relative poverty - 15% of this section of the population - which is up by 70,000 from 2011-12.
The number of pensioners living in relative poverty also increased by 10,000 in 2012-13 to stand at 150,000, with 15% of senior citizens affected.
The figures also show that more than half (52%) of working age adults who were in poverty were in work, with some 250,000 people in this position in 2012-13.
Meanwhile, 110,000 children in poverty were living in families where at least one adult was in work, meaning 59% of youngsters in poverty were in working households.
The average income in Scotland fell to £23,000 in 2012-13, a drop of £400 from the previous year.
A couple with no children are classed as being in relative poverty if their income is £13,800 or less - the equivalent of £264 a week.
Ms Sturgeon said: "The Scottish Government has focused on doing everything we can to mitigate the harmful effects of Westminster welfare cuts - and we will continue to do so - but the impact is still being felt by the most vulnerable in our society.
"What is even more worrying is that 70% of the welfare cuts are still to come - Scotland will see its welfare budget reduced by over £6 billion by 2015-16. And some estimates suggest that up to 100,000 more children could be living in poverty by 2020 if we continue with Westminster policies. In other words, the unacceptable increase in the number of children living in poverty revealed by today's statistics could be just the tip of the iceberg."
She continued: "These figures show incomes are falling for families in Scotland. Our 'social contract' policies and our efforts to mitigate the impact of welfare cuts are designed to help, but we need the powers to do more.
"In an independent Scotland we would have the powers to provide one of the most comprehensive child care packages in Europe which would allow more parents to work. We would also be able to set up a commission to consider a new 'Scottish Minimum Wage' - which would at least rise in line with inflation - and ensure that benefits, allowances and tax credits keep rising with the cost of living.
"Today's figures demonstrate just how vital the full powers of independence now are, to enable us to create a different approach - one that supports our most vulnerable, encourages people into the workplace and provides a fair day's pay for a fair day's work."
Anti-poverty campaigners demanded the governments in Edinburgh and London do more to help those struggling to get by.
Peter Kelly, director of the Poverty Alliance, said the rise in poverty was "extremely disappointing", and added: "We are especially concerned that the previous downward trends in child poverty figures has been reversed.
"Much of this is due to the policies being pursued by the current UK Government. Regressive tax policies and punitive welfare reform measures are pushing more and more people into poverty.
"People in Scotland and the UK quite simply don't have enough money to live on.
"We need to see a meaningful increase in benefit levels and both governments need to do more to create quality, well paid jobs.
"It is unacceptable that over half (52%) of working age adults in poverty were in households where someone was in work, and 110,000 children in Scotland were living in households affected by in-work poverty.
"People should not work for their poverty, and deserve to be properly paid for their work.
"These are not just statistics, these are people's lives. We need to remember this when developing the policies needed to address poverty, and put those with experience of poverty at the heart of finding the solutions to the problems.
"Governments at the UK and Scottish levels need to take action now to ensure that we don't see further increases in the future."
John Dickie, head of Child Poverty Action Group, said: "These shocking figures mark the turning of the tide on child poverty as UK Government tax and benefit policies slash family incomes at the same time as wages stagnate.
"After years of real progress, 30,000 more children have already been pushed into poverty in Scotland and massive increases are forecast for the years ahead. UK ministers need to come out of their denial and produce a child poverty strategy that boosts rather than cuts family incomes, whilst here in Scotland ministers need to translate the Scottish Child Poverty Strategy into the improved wages, services and support that families need in the face of unprecedented pressure on their incomes.
"Behind these statistics are tens of thousands of children across Scotland who, despite their parents' best efforts, will see their health undermined, education damaged and life chances thwarted unless government at every level acts with the utmost urgency."
Neil Mathers, of Save the Children Scotland, said: "Today's figures are bad news. They show 30,000 more children living in low income households in Scotland and confirm our worst fears that poverty is on the rise and tens of thousands more children will suffer as a result.
"The figures highlight that six out of 10 children in poverty are living in working households. This represents an increase over 11% over the last decade.
"Reducing child poverty should remain a priority for all levels of government in Scotland. The welcome ambitions in the Child Poverty Strategy for Scotland need to be translated into action in the labour market and across local services that support families, such as supporting parents to access good quality jobs and further improving the affordability and availability of childcare.
"We call on the UK Government to take urgent steps to help families with young children to meet essential living costs."
A spokesman for the UK Department for Work and Pensions (DWP) said: "The UK Government is committed to ending child poverty by tackling its root causes, including worklessness, low earnings and educational failure. Under this Government there are 300,000 fewer children living in relative income poverty and 290,000 fewer children in workless households across the UK.
"As part of our long-term economic plan, we have seen the largest rise in employment for over 40 years and unemployment is falling. Relative child poverty in Scotland has fallen since the mid-1990s and is lower than 2009-10 levels.
" We are making the welfare system affordable for the long term while supporting the living standards of poor families by freezing fuel duty, increasing personal tax allowance and cutting income tax for those on the minimum wage by almost two thirds."