Politicians and campaign groups have criticised four branches of the supermarket chain Centra for offering cut price alcohol among products marketed as Children's Allowance day deals.
The promotion was referred to several authorities, including the Office of the Director of Consumer Affairs.
Centra said it takes the sale and promotion of alcohol very seriously and it has instructed the retailers involved to withdraw the promotion.
A flyer was circulated by stores in Fairview and East Wall in Dublin, one store in Kilcoole, Co Wicklow and another in Tullamore, Co Offaly.
Two cheap alcoholic drinks were advertised alongside reduced price biscuits, pizza and ice cream.
Alcohol Action Ireland Director Fiona Ryan described the promotion as "totally irresponsible", especially when "one in 11 children in Ireland are living with a parent with problematic alcohol use".
In the Dáil, Taoiseach Enda Kenny described it as "exceptionally irresponsible".
Barnardos said the campaign sent out the wrong message about what child benefit is designed to do.
Chief Executive Fergus Finlay said: "This promotion is insulting to parents and families all over Ireland who are already struggling to provide for their children."
The campaign also drew criticism from Fianna Fáil's Senator Averil Power and Councillor Nick Killian.
Centra said: "The promotion is not part of a national marketing plan or promotional strategy
"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.
"The promotion undermines our genuine commitment to take our social responsibilities regarding alcohol extremely seriously."
In a statement, Minister for Social Protection Joan Burton pointed out that Child Benefit is for the benefit of children.
She said that targeted promotions of cheap alcohol are inappropriate where they divert badly needed funds from children and families.