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.
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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."
A DWP spokesman 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."