Proposals were put forward by Irish Health Minister Leo Varadkar earlier this week which would make it illegal to sell drink below a set price in the Republic.
Neil Johnston from Chest Heart and Stroke said: "We believe the Health Minister and the Northern Ireland Executive must follow suit, primarily for health reasons, but also to reduce the potential for alcohol smuggling if there were a large price differential between the two parts of the island."
Health Minister Jim Wells has said he supports the introduction of minimum alcohol pricing.
He said excessive drinking costs the NI economy as much as £900m per year, including costs amounting to £240m on healthcare.
In a statement, the Department of Health said the minister welcomes the decision by the Irish government and plans to launch a public consultation for Northern Ireland.
Source: UTV, 05/02/15