The progress of the proposed ban is being watched intently by tobacco manufacturers who fear it could have worldwide implications.
Under the proposal smokers would need a valid medical certificate to buy tobacco products, which would only be available from pharmacies.
Smokers – who would be referred to as 'patients' - would also need to submit to regular health checks.
Siv Fridleifsdottir, Iceland's former health minister, who is bringing the private members' bill said the nation needed to "wake up" to the dangers of smoking.
But the success of the bill is by no means assured.
Anna Baldursdottir, spokeswoman from the ministry of welfare, said: “Siv Frideleifsdottir is a very serious politician and this is a very serious proposal.
“Whether it not it eventually becomes law, I do not know. I seriously doubt it.”