Therese Coffey has been criticised after suggesting people struggling to afford food could work more hours or upskill to get a higher income.
Labour MP Rachael Maskell accused the environment secretary of blaming people on low wages for their food poverty.
“It is time her government supported families in need, not making them work harder for a crust,” she said.
Food inflation is at a 45-year high, with grocery prices 16.7% higher than last year.
During a question session in the House of Commons, Ms Maskell told MPs that food banks in her York constituency were running out of supplies and asked what the government was doing “to ensure that no one goes without”.
Ms Coffey replied that inflation was “really tough at the moment” but noted the UK had “one of the lowest proportions of incomes being spent on food” in Europe.
She said people could also access the £842m Household Support Fund before adding: “We know that one of the best ways for people to boost their income is not only to get into work if they are not in work already, but to work more hours or get upskilled to get a higher income.”
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Speaking after the question session, Ms Maskell said: “It is shocking that the environment secretary shifted blame for food poverty onto people because they are on low wages and are poor, expecting them to work even more hours to put food on the table.”
Another Labour MP, Nadia Whittome, said the comments showed that the government was “utterly out of touch with working class people”.
Ms Coffey has also come under fire for suggesting turnips were an alternative to seasonal vegetables that are running short in shops.
Asda, Morrisons, Aldi and Tesco have limited sales of certain fruit and vegetable items, following supply problems partly caused by extreme weather in Spain and north Africa.
Ms Coffey said she expected the situation to last another two to four weeks and that ministers were talking to retailers about how to avoid problems in the future.
During an urgent question on the subject, Conservative MP Selaine Saxby suggested consumers could avoid issues by “eating more seasonally and supporting our own British farmers”.
Ms Coffey replied: “Many people would be eating turnips right now rather than thinking necessarily about lettuce, tomatoes and similar.
“However, I am conscious that consumers want a year-round choice, and that is what our supermarkets, food producers and growers around the world try to satisfy.”
Liberal Democrat leader Sir Ed Davey summarised the minister’s response as “let them eat turnips” – a reference to 18th century French queen Marie Antionette, who supposedly responded to concerns that the population had no bread by saying: “Let them eat cake.”
A spokesman for the prime minister said: “What the secretary of state was doing was setting out the importance of celebrating the produce that we grow here in the UK.”
“We don’t believe it’s for us to tell people what they should or shouldn’t buy,” he added.