Mark Drakeford says the Welsh Government will do 'everything it can' to help people facing the choice between heating or eating.
The First Minister has said families in Wales have "good reason" to be scared as the cost of living crisis deepens.
Speaking to ITV Cymru Wales, Mark Drakeford acknowledged that some will face the "awful choice between starving or freezing".
With the energy price cap rocketing up by 54%, a national insurance tax increase and prices on things like fuel and food rising, the Office for Budget Responsibility has said we are facing the biggest fall in living standards in the UK since records began.
The Welsh Government has outlined how it will use £380 million to help with rising costs and Mr Drakeford added that people have already started to feel the benefit of financial support systems put in place.
However he shouldered responsibility for the cost of living crisis on the UK Government, saying it "refuses to use the powers it has to help people".
The Secretary of State for Wales, Simon Hart, has previously defended the UK Government's decisions and said it was doing "absolutely everything" it can to help people in Wales cope with the cost of living.
In an interview with ITV Cymru Wales' Cost of Living Correspondent, Carole Green asked the First Minister what he would say to people across Wales who are scared for what's to come.
Mr Drakeford replied: "I'm afraid I'd say that there is good reason for that, there will be families here in Wales who are faced with that awful choice between starving or freezing.
"The Welsh Government will do everything we can to help those people. With all the things that we have done over the past few weeks - 380 million pounds worth of a package that is all directed to trying to make a difference."
He added that people are already seeing the impact of some of those measures.
"I'm meeting people who've already had the £200 we've been able to provide to help people with their fuel bills in the winter we're just coming out of," he said.
"And people will be seeing, in the next weeks, the £150 that they will be getting as a result of the decisions we've made on council tax."
Mark Drakeford also blamed the UK Government for the cost of living crisis and said decisions made by the Chancellor will increase child poverty here in Wales.
He said measures ministers in Cardiff Bay have taken to help those on low incomes only have full effect "if you have a UK Government willing to work with you, rather than the current government which refuses to use the powers it has to help people”.
Commenting on whether both governments were passing the buck on blame, Mr Drakeford insisted that was not the case.
He said: "It's not passing the buck to point out that in September last year, the UK Government took £20 a week away from the poorest families in the land who relied on Universal Credit. That was a deliberate choice that they made.
"It's not passing the buck to point out that that the Chancellor's own documentation, ten days ago in the spring statement, said that the action he was taking would result in half a million more children across the UK living in poverty than would have if he had taken other choices.
"The tides that they are setting in motion will create more child poverty here in Wales."
On Monday (April 4), UK Government minister and Secretary of State for Wales, Simon Hart defended Rishi Sunak's spring statement.
Mr Hart said: "In my view what he's done, for now and he's stressed for now, is to go as far as he reasonably can. He hasn't ruled out further measures...he went as far as he thought he safely could for now to protect families and business across the country."
He added the UK Government was doing everything it can to help families facing the choice between eating and heating and said the Conservatives' handling of the economy over the past decade had resulted in tangible economic growth.
"What we've been able to do by managing the economy in a sensible and professional manner is to make sure that we are the fastest growing economy in the G7 at the moment in a post-pandemic world," he said.
"The economy is driven and survives on decent, sustainable jobs, that's what enable us to look after as best as we possibly can either the elderly or people in more challenging circumstances."
Responding to comments made by the First Minister, Welsh Conservative Leader Andrew RT Davies MS, said Labour Governments in Wales have continually "blundered their way though economic policy".
He said: "There isn’t a country in the world that isn’t being affected by the cost of living crisis. I am extremely disappointed to hear the First Minister’s comments considering Labour’s embarrassing record. This is just another example of Labour passing the blame and avoiding responsibility.
"For 23 years, successive Labour Governments in Cardiff Bay have blundered their way from one failed economic policy to another leaving a quarter of the Welsh population in poverty and with wage packets £60 a week lighter than elsewhere in the UK.
"Labour ministers in Cardiff Bay need to stop playing politics and use devolved levers to support aspiration and create the well-paid, skilled jobs that people need."