In one video All Blacks and Blues forward Steven Luatua pours a beer down the throat of another man, who spills the beer down his chin as he drinks and is cheered on by others in the room.
The 22-year-old player said it was a poor decision to become involved in the game which occurred at a private function.
"I'd like to apologise for any harm my involvement may have caused. When asked to participate I went along with it but in hindsight I should have dealt with the situation a lot more responsibly."
He said he was unaware of what the game itself involved and did not condone irresponsible or dangerous drinking.
Blues head coach Sir John Kirwan said it was a disappointing error of judgment.
"I've spoken to him about it and he's deeply apologetic. It's very uncharacteristic of him as he is a great role model and has always set a good example to others."
Blues CEO Michael Redman said there were social media and alcohol policies, alongside education and awareness programmes, for players.
The craze has quickly gained popularity. A "Neknominations NZ" Facebook page, started less than a week ago, had almost 6500 "likes" last night.
Alcohol Healthwatch director Rebecca Williams said the "worrying" game was promoting excessive and quick consumption of alcohol, made even more troubling due to the element of competition.
"To me it could very well end in something quite tragic," Ms Williams said.
