Alex Neil spoke out as the Scottish Government's controversial policy, which aims to set a 50p floor price per unit, is due to be tested again at the Court of Session in Edinburgh following a legal challenge from the Scottish Whisky Association (SWA).
He argued it is not right that a man can buy a week's worth of drink within the "sensible" drinking guidelines for less than £5.
However, some within the industry say the policy will not deal with alcohol abuse effectively and could put up global trade barriers.
Neil said: "Each week on average in Scotland, alcohol misuse is responsible for more than 20 deaths and 700 hospital admissions. Being able to buy 20 units of alcohol for the change in your pocket is just unacceptable.
"It shows that this kind of high-strength alcohol - the type which does much of the damage - has become far too cheap in Scotland.
"Time and time again the research proves that affordability is the key factor in the misuse of alcohol and that the most effective way to tackle this is by setting a minimum price."
Neil added: "Minimum pricing would begin saving lives within months of its introduction and while it is regrettable the policy is being subject to delays as a result of the legal challenge, the Scottish Government remains absolutely committed to bringing in legislation that would set the minimum price for a unit of alcohol at 50p."
He pointed to research showing that it is possible to buy three litres of branded high-strength cider, equivalent to around 22 units, for £4.50. Twelve cans of lager - at 21 units - are being sold for £8, while 26 units of supermarket-brand vodka is available for less than £11, the Scottish Government claims.
A legal challenge by the SWA to minimum pricing was rejected in May last year. The association appealed against the ruling, pitting the two side=s against each other again in court this week.
The SWA says minimum pricing is a regressive policy that hits responsible drinkers, particularly those on lower incomes. It also notes the UK Government decided against pursuing a similar policy because of a lack of "concrete evidence".
Rosemary Gallagher of the SWA said: "Minimum unit pricing is an unfair and untargeted policy that penalises responsible drinkers, especially those on lower incomes. It impacts poorer people and will have little effect on the highest earners who make up the majority of hazardous and harmful drinkers.
"The Scottish Government's own report says 'the main driver of increasing affordability has been rising disposable incomes'. But while affordability may have risen, alcohol-related harms and deaths have been falling in Scotland in recent years."
She argued that measures in place to tackle problem drinking are working and that numbers are falling for those being treated in hospital for alcohol-related issues.
She added: "Deaths have fallen 36% from a peak in 2003. This would suggest measures in place are already working.
"Figures published just this week by NHS Scotland show that in 2012-13, there were an estimated 94,630 alcohol-related primary care consultations by 48,420 patients, a substantial fall from 109,170 consultations by 57,470 patients in 2011-12."