Asda's Skol offer, which works out at 51p a litre, makes the lager almost half the price of water with a four pack of Evian costing £2.91 or 97p a litre.
Don Shenker, the chief executive of Alcohol Concern, said: "These low prices have a real impact on under-age drinkers and on heavy drinkers from lower social groups.
"Major chains such as Asda have a responsibility to weigh up in their minds the impact of these kind of promotions. The fact of the matter is price is a crucial determinant of how much we drink."
Dr Vivienne Nathanson, head of science and ethics at the British Medical Association, said: "Alcohol abuse is a public health emergency. People need to be prepared to look at an increase in price."
Asda defended its Skol offer and pointed out that its cheapest water is 15p for two litres.
A spokesman for the supermarket said: "We take our role as a responsible retailer very seriously. A ban on promotions and the introduction of minimum pricing will simply create incentives for black markets."
Supermarkets and off licenses came under fire for cheap alcohol last year when 193 MPs called on them to "end irresponsible drinks promotions and agree not to use alcohol as a loss leader".
Earlier this year Asda banned the sale of alcohol in its town centre stores overnight and stopped selling certain alcopops and shooters that appeal to young people.