The craze, which has been implicated in several deaths, involves people filming themselves downing alcohol, nominating someone to continue the game, and posting the video on Facebook.
The Neknominate Facebook page, which has more than 8,000 "likes", has the headline "it's not a crime to get drunk".
The industry-funded charity Drinkaware is calling on parents to take a tough stance against the game amid fears the trend could spread to young teenagers.
Research suggests that children are more than twice as likely to have an alcoholic drink if they have felt encouraged to do so.
Elaine Hindal, chief executive of Drinkaware, said: ""Young people should also be reminded that the behaviour of some older teens taking part in social media drinking games is not something to be copied - it can have serious implications. We believe it's better to have the 'alcohol chat' in the living room than in A&E."