The scheme, part of the government's Change 4 Life 'Really Big Summer Adventure' initiative, involves making available five million vouchers over the internet, in newspapers and in Asda branches.
The scheme is part of the government's bid to crack down on obesity by offering discounts on healthy foods.
The scheme offers families discounts totalling £50 from a range of food products from Asda.
Included in the offers are discounts on products like Kellogg's Rice Krispies and Warburton's bread sold in Asda.
Sustain, the campaigning group, has labelled the scheme "costly", "short-term" and tokenistic".
Charlie Powell, campaign director at Sustain, said: "Given the UK's unenviable position at the top of Europe’s obesity league table, we urgently need measures that tackle the root causes of the problem.
"Instead, we are offered another costly, short-term, tokenistic voucher scheme which provides a great advertising opportunity to the food companies involved, but which has no hope of changing people’s long-term behaviours.
"Until the government regulates to protect children from junk food marketing it has to shoulder the blame – alongside companies that promote fatty and sugary products – for the alarming rates of childhood obesity."
But sources close to the Department of Health said they were disappointed by Sustain's response and that the initiative represented good value for money.
Asda was unavaible for comment.
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