The Tory MP said the charity was meant to look after people in the poorest countries and should be "ashamed".
It comes after Unicef said it would pledge £25,000 to a south London charity to help supply breakfast boxes over the Christmas holidays.
Unicef said every child deserves to "thrive" no matter where they are born.
The grant to the charity School Food Matters aims to help vulnerable children and families during the coronavirus crisis.
Unicef said the initiative was its first emergency response in the UK in its 70-year history.
Mr Rees-Mogg was responding to a question from Labour MP Zarah Sultana in the House of Commons.
"For the first time ever, Unicef, the UN agency responsible for providing humanitarian aid to children, is having to feed working-class kids in the UK," she said. "But while children go hungry, a wealthy few enjoy obscene riches."
She asked if Mr Rees-Mogg would "give government time to discuss the need to make him and his super-rich chums pay their fair share so that we can end the grotesque inequality that scars our society".
Responding, Mr Rees-Mogg said Unicef "should be ashamed of itself".
"I think it is a real scandal that Unicef should be playing politics in this way when it is meant to be looking after people in the poorest, the most deprived, countries of the world where people are starving, where there are famines and where there are civil wars, and they make cheap political points of this kind, giving, l think, £25,000 to one council," he said.
"It is a political stunt of the lowest order."
He said the number of children in absolute poverty across the country had gone down by 100,000 over the past decade, which he described as "a record of success".
In response, Anna Kettley, Unicef UK's director of programmes and advocacy, said: "Unicef UK is responding to this unprecedented crisis and building on our 25 years' experience of working on children's rights in the UK with a one-off domestic response, launched in August, to provide support to vulnerable children and families around the country during this crisis period."
She said more than £700,000 was being granted to community groups around the country to help tackle food insecurity during the pandemic.
"Unicef will continue to spend our international funding helping the world's poorest children. We believe that every child is important and deserves to survive and thrive no matter where they are born," she added.
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