The Charity Commission is assessing whether a promotional campaign by Oxfam broke its rules by criticising the government's austerity programme.
The charity put out a tweet speaking of a "perfect storm" caused by "zero hours contracts, high prices, benefit cuts, unemployment and childcare costs".
It is part of a wider campaign by the charity blaming welfare cuts for the increased use of food banks.
A Conservative MP said he was "shocked" by the "overtly political" campaign.
But Oxfam insisted that drawing attention to poverty and tackling it "should not be a party political issue".
Oxfam claim that more than 20 million meals were delivered to people living in poverty by the four main food bank charities last year.
The aid charity is getting constituents to email MPs with a letter that highlights what it says is the "unacceptable" reliance on food banks by a growing number of people.
The letter cites a number of reasons for food banks' prevalence including "low incomes, rising living costs, welfare cuts, and problems with the benefit sanctions system that stops vital welfare payments going to people who are struggling to make ends meet".
It urges the government to keep track of the number of people using food banks and encourages constituents to press their MPs to "highlight the need for urgent action to address the rise in food poverty".
Conor Burns, the Conservative MP for Bournemouth West, has asked the Charity Commission to urgently investigate whether the campaign breaches the organisation's charitable status.
In a letter to its chair William Shawcross, Mr Burns said the campaign was "overtly political and aimed at the policies of the current government".
Speaking later, he added: "Many people who support Oxfam will be shocked and saddened by this highly political campaigning in domestic British politics.
"Most of us operated under the illusion that Oxfam's focus was on the relief of poverty and famine overseas.
"I cannot see how using funds donated to charity to campaign politically can be in accord with Oxfam's charitable status."
He said he had received a reply from Mr Shawcross in which he said that "the tweet is currently being assessed to see whether it raises any regulatory concerns".
A Charity Commission spokeswoman said it had received a complaint about the campaign but had contacted the individual concerned for more information about the basis of their objections.
"It is worth being aware of the rules on charity campaigning," she added. "Charities are often the most appropriate organisations to speak out and campaign on behalf of their users.
"From lobbying politicians to running online petitions, charities can engage in a range of activities to support their charity's aims. But charities must never be politically biased or support a politician."
Ben Phillips, Oxfam's campaigns and policy director, said it was a "resolutely non-party political organisation".
"We have a duty to draw attention to the hardship suffered by poor people we work with in the UK," he said.
"Fighting poverty should not be a party political issue. Successive governments have presided over a tide of rising inequality and created a situation where food banks and other providers provided 20 million meals last year to people who could not afford to feed themselves.
"This is an unacceptable situation in one of the world's largest economies and politicians of all stripes have a responsibility to tackle it."