The foundation was set up last year to support charities working to prevent young people abusing alcohol and drugs. The Big Cold Turkey is its first national campaign and was launched on Monday with an advertisement in The Big Issue magazine.
The ad calls for celebrities to give up a "vice of their choice", which could be anything from cocaine to coffee, for 42 days.
Celebrities will be asked to donate an entry fee of between £2,500 and £10,000 in order to take part. Those who give in to temptation will have to make the same donation and start again.
Marksteen Adamson, the founder of the Big Cold Turkey Foundation, said: "We are hoping to attract celebrities who are role models for young people.
Someone such as Kate Moss carries a huge influence and it would be great if she could take part."
Moss has not yet responded to the invitation.