He will say the measure will save lives in Scotland if it gets the go-ahead.
In a verdict that could lead to a lengthy fight in the European Court of Justice, the commission last week judged the policy to be in breach of European free trade laws.
Catherine Day, the EU's top official, said plans to enforce a minimum price of 50p per unit of alcohol would discriminate against French brandy imports and European drinks companies which needed to offer discounts to establish a foothold in the Scottish market.
Speaking before his visit to Brussels, Mr Neil said: "Minimum pricing has been agreed by Parliament and backed by expert opinion. We believe the introduction of minimum pricing will be an effective and efficient way of tackling alcohol misuse, targeting those that are drinking the most.
"The point that I will make in Brussels is that minimum pricing can and will save lives.
"Recent studies have shown that hospital discharges have quadrupled since the early 1980s and deaths have more than doubled. Scottish alcohol sales have increased by 10% since 1994 and are now 20% higher per person than in England and Wales."
Mr Neil added: "Alcohol misuse is costing Scotland too much: potentially around £3.6 billion per year in extra services and productivity, a staggering figure that equates to £900 for every adult in our country.
"I firmly believe serious action is required to rebalance our unhealthy relationship with alcohol. That is why we remain absolutely committed to introducing minimum pricing in Scotland."
The commission said it would prefer a wholesale increase in all alcohol prices through raising taxes, something outwith Holyrood's control, or unspecified targeted measures in the specific Scottish regions where alcohol abuse is a problem, rather than penalising the entire population.
The EC directive asks the Scottish Government to "abstain from adopting the draft legislation at issue".
The UK Government, as the EU member state, has until December 27 to make a formal response. However, the Scottish Government will present the case.
Prime Minister David Cameron has proposed a 45p per unit minimum alcohol price in England and ministers there say they will stand "shoulder to shoulder" with Holyrood counterparts in challenging the Brussels ruling.
A 50p per unit minimum price would make it illegal to sell a standard 70cl bottle of whisky for less than £14. A normal-strength bottle of wine would be at least £4.69.
Scotland's minimum pricing move attracted opposition from other EU countries including Italy, France, Spain and Bulgaria before the commission gave its own verdict. Drinks industry bodies across the Continent have also challenged the proposal, claiming it would not achieve the claimed health benefits.
In her "detailed opinion" EC general secretary Ms Day noted that most French brandy sold for less than 50p per unit while only a small proportion of whisky came in below the proposed minimum price.
She also cited the examples of Irish and Swedish ciders which were able to compete in the Scottish market thanks to initial special offers.