Four Centra stores were ordered to withdraw the “cynical” offers after politicians and children’s groups raised concerns.
Justice Minister Alan Shatter said the inclusion of beer on the leaflet was irresponsible and reprehensible.
“It suggests that some retailers are more concerned with boosting their turnover and profits than selling alcohol responsibly,” said Mr Shatter.
“I am also shocked at the suggestion that allowances paid by the State for the benefit of children should be targeted in such a cynical manner by the retailers concerned.”
Joan Burton, Social Protection Minister, said child benefit is for the benefit of children.
“Targeted promotions of cheap alcohol are inappropriate where they divert badly needed funds from children and families,” she added.
The Centra shops in Fairview and East Wall in north Dublin, Kilcoole in Wicklow and Tullamore in Offaly distributed flyers headlined “Children’s Allowance Day Deals” and featuring a range of price promotions, including a three-day deal on bottles of Miller and Budweiser.
Centra said the promotion was not part of a national marketing plan, adding the four franchised stores were immediately ordered to withdraw it.
“Centra fully understands that the abuse of alcohol is a serious issue in Irish society and apologises for the promotion, which although isolated to four stores, is contrary to Centra’s belief that retailers have a critical role to play in ensuring that alcohol is promoted and sold responsibly,” said a spokesman.
“As a community brand, we are acutely conscious of our corporate and social responsibilities.
“We accept that there is a problem with alcohol consumption, binge drinking and alcohol-related health and public order problems.”
Children’s charity Barnardos and Alcohol Action Ireland criticised the campaign, which they claimed was irresponsible and sent out the wrong message about child benefit.
It is estimated one in 11 children in Ireland live with a parent with an alcohol problem.
Roisin Shortall, Minister of State, said it was deeply disturbing a retailer would promote alcohol that way.
“Alcohol causes almost 90 deaths every month, is responsible for a quarter of injuries presenting to our emergency departments and is a trigger in one third of domestic abuse cases,” said Ms Shortall, who is trying to tackle Ireland’s drinking culture through an action plan.
“The Centra promotion illustrates the weakness of a voluntary code in this area.”
Fianna Fáil Senator Averil Power said she was shocked to see a respected company and brand name like Centra associated with such a cynical and reckless promotion.
Ms Power, who was first to call on Centra to pull the promotion, plans to write to the Office of the Director of Consumer Affairs, the Advertising Standards Authority of Ireland, retail groups and the ministers for health and social protection.
“This campaign was insulting to parents, many of whom are finding it harder every day to meet their commitments to their households, and for whom alcohol promotions are the last thing on their minds,” she added.
Centra said it complies with the law and the Responsible Retailers of Alcohol in Ireland (RRAI) code, which it believes should be put on a statutory footing.
