They were taken to the Balfour Hospital in Kirkwall after allegedly taking part in the craze that involves downing a drink quickly, posting the video online and then nominating others.
The local health board refused to disclose details.
But NHS Orkney's Director of Public Health, Dr Louise Wilson said: "We are very concerned about young people putting themselves into danger.
"Mixing high volumes of alcohol and consuming quickly can prove fatal, particularly in young people. We certainly don't want the Orkney community to experience a tragedy as a result of this 'game'."