Barrett has 417,000 Instagram followers and McKenzie has 186,000.
Alcohol Healthwatch director Nicki Jackson complained that the photos breached two rules in the code:
• Alcohol advertising and promotions in non-restricted areas shall not use or refer to identifiable heroes or heroines of the young.
• Anyone visually prominent in alcohol advertising and promotions depicting alcohol being consumed shall be, and shall appear to be, at least 25 years of age.
Damian McKenzie, who turns 24 next month, is under age 25.
Complaints Board chairwoman Raewyn Anderson upheld the first complaint.
"All Blacks have been designated heroes of the young in previous Complaints Board decisions," she said.
But she did not rule on the complaint about McKenzie's age, noting that Tennis Auckland had removed the photos from the Instagram accounts of the two All Blacks and the ASB Classic after she forwarded Jackson's complaint to them on February 11.
Tennis Auckland and Moet & Hennessy also told her that they would discuss the breach in their formal debrief of the tournament and had circulated copies of the code to all relevant staff.
She ruled that the matter had been settled.
"Taking into account the self-regulatory action to promptly remove the advertisement and the undertaking, through education, to minimise the risk of a reoccurrence and another code breach, it would serve no further purpose to place the matter before the Complaints Board," she said.
Moet & Hennessy NZ senior brands manager Juliet McInnes said the company "took immediate and incisive action and had the images taken down".
"We apologise to all concerned and we will be more alert in future," she said.
However Jackson said the case showed that New Zealand's system of industry self-regulation of alcohol advertising did not work because the photos were on Instagram from January 7 until February 12 when they were finally removed.
"It's too late. The damage has already been done, the harm has been done, and that's not good enough," she said.
"I detected this ad a week or two after it was put up. It was 37 days out on the internet to be exposed to young people."
She said the guidelines were "purely voluntary" and there were no financial penalties for breaches.
She urged the Government to put the code into law, as it did for tobacco in 1995 and has been recommended for alcohol by the Law Commission in 2010 and by a ministerial forum on alcohol advertising and sponsorship in 2014.
NZ Rugby has so far resisted attempts to end alcohol sponsorship of the sport.
The head of the marketing department in the University of Auckland's Business School, Dr Bodo Lang, said "social media influencers" in Germany could earn 6000 Euros for a single social media post promoting a brand.
"The first value is brand awareness. "Before you saw that post you wouldn't have thought of Moet champagne," he said.
"Immediately after that post, your brand awareness has gone up probably 100 per cent, so you are aware of the brand and you think, 'I'm taking my wife out to dinner,' or 'I'm going to the footy club with my mates,' and so that brand becomes much more likely for you to purchase."
Secondly, he said the appeal of celebrities such as All Blacks rubbed off on the brand.
"When you look at the brand at the liquor store, you think, 'This is the drink that champions drink.'"
Souter said the advertising code permitted showing the logos of alcohol companies that sponsor sports, but not the alcoholic products themselves. The Instagram posts of Barrett and McKenzie pouring champagne were deemed to be "alcohol advertisements" because they showed the product.
The All Blacks are sponsored by Steinlager and Lang said its sponsorship deal was likely to include a exclusivity clause barring All Blacks from promoting other alcohol brands.
