The referendum marks the second controversial popular initiative this year put forward in the Catholic principality, after another vote in June which led to the recognition of civil partnerships for homosexuals.
The 18,800 electors in the tiny Alpine state will be asked to vote on whether abortion within 12 weeks of conception should be legalised, in a proposal titled Help rather than Punishment.
Currently, a termination of pregnancy carries a penalty of up to a year in prison even if it is carried out abroad.
But even if voters agree to the move Prince Alois has already said he would not sign the text into law. Liechtenstein's government and parliament are also opposed to it.
The prince said he was opposed to such legislation because it could be misused to prevent the births of handicapped children.
His grandfather, prince Franz-Josef II, set a precedent in 1961 when he refused to approve a referendum result reforming the right to hunt in Liechtenstein.
Proponents of the text point out that Liechtenstein's neighbours, Switzerland and Austria, both authorise abortion.
They also claim that 50 women break the law every year in their country, or head to Swiss cities such as Chur or St Gallen to carry out abortions.
The UN has repeatedly asked Liechtenstein to stop criminalising abortion.