The game involves participants downing large amounts of alcohol in often bizarre places and posting a video on Facebook before nominating someone to continue the game.
More than often, those taking part are attempting to drink dangerous levels of alcohol, such as pints of whiskey or vodka, or large cocktails of spirits and lager or beer at the same time.
Two British men, one from Cardiff and one from London, and two men from Ireland, are all believed to have died as a result of playing the game in recent weeks.
Notts chief inspector Linda McCarthy said: “The neknominate craze is certainly worrying and we are keen to warn people of the very real dangers associated with this kind of extreme drinking.”
“The deaths of young people in recent days and weeks, which have been potentially linked with the game, is shocking.”
“So it is of vital importance that we highlight the risks.”
“I do not want Notts officers to be delivering death messages to parents and families of young people who have died needlessly.”
“Don’t let this happen to you and don’t let this happen to someone in your family.”
Derbyshire police have also expressed their concerns over the game and urged young people not to take part.
“Drinking large quantities of alcohol in a short space of time can have very serious consequences ,” said a spokesman.
“I would like to urge the public to act responsibly and not to take part.”
“Not only are the people taking part putting themselves in unnecessary danger, they could also face prosecution as it is an offence to act disorderly in a public place.”