The Local Government Association (LGA), which represents almost 400 councils in England and Wales, is calling for Facebook and Twitter to put messages on their sites outlining the risks, similar to the warnings printed on cigarette packets.
NekNomination has seen social media users film themselves drinking large amounts of alcohol before posting the footage online and nominating a friend to repeat the dare.
As well as alcohol, videos posted have shown people consuming dog food, motor oil and even live goldfish – and the craze is believed to have so far claimed five lives in the UK.
Councils are planning internet safety campaigns, while schools have requested warning notices for notice boards and to be read out at assemblies.
LGA Community Wellbeing board chairwoman Coun Katie Hall said: “This is an utterly reckless and totally irresponsible craze which has tragically claimed lives. More should be done to highlight the dangers and persuade people not to participate.
“We believe social media operators have a responsibility to provide health warnings to user groups and individuals.”
She said she wanted to meet with Facebook and Twitter executives to discuss a way to tackle the issue head on.