At the $1.20 setting, the policy would lead to "conservative" net savings of $624 million over ten years as a result of reduced crime and improved health and workplace productivity.
"A minimum price or excise increase would have some impact on low risk drinkers, but the savings to society significantly outweigh the lost benefits to consumers," the report's authors said.
The ministry also expressed some reservations.
Minimum pricing had only be trialled in some Canadian provinces and in Scotland.
Harmful drinkers bought from across the price spectrum and some would not be captured by the regime. And a price point of $1.20 per standard drink would generate an additional $131 million per year for the liquor industry.
The ministry recommended that a minimum pricing regime should not be considered for five years. It said this would give time for Government to assess the impact of alcohol reforms which passed in late 2012.
Opposition MPs described those reforms as toothless and had lobbied for a floor price to be included in the law changes.
Minimum pricing was designed to raise the price of low-cost, high-strength drinks.
Raising the minimum price of alcohol to $1.20 would affect a quarter of alcohol sales. A $7 bottle of wine would rise to $8.60 and a $10 12-pack of beer would rise to $18.40.
An $18 bottle of wine would remain the same price.
The investigation of a minimum pricing regime was a recommendation of the Law Commission, which said in a landmark review of alcohol harm that price was one of the most effective deterrents of alcohol abuse.
It said a 50 per cent increase in excise tax would be more effective than a floor price, but National immediately ruled out a tax hike.