Human rights groups in Tunisia had also campaigned for the law's abolition.
The order comes into force immediately and couples are free to register their marriages at government offices.
An important milestone
Rana Jawad, BBC News, Tunis
Many Tunisians see the removal of the marriage restriction as another landmark in guaranteeing women's freedom in the country.
It sets apart Tunisia as the first country in the Middle East and North Africa to remove the legal hurdles to marrying outside the official state religion.
It is an important milestone in a region where religion in marital ties can be at the heart of many a family feud, and long struggles against state laws.
Unlike Muslim women, men can marry non-Muslim women without providing any religious documents.
Tunisia is also home to a Jewish, as well as a small Christian, minority and it is not entirely clear how the marriage restriction applied to them.
Scrapping the decree may not do away with the cultural and traditional obstacles women face with their families in cases of inter-faith marriage, but it now offers Tunisian women greater freedom of choice from a legal perspective.
In July, the Tunisian parliament also introduced a new law that abolished a clause that allowed rapists to escape any punishment if they married their victims.
The country banned polygamy as far back as 1956, setting it apart from other Muslim-majority nations.
However, women in Tunisia still face discrimination, particularly in matters of inheritance which still prioritises sons over daughters.
The Tunisian Association of Democratic Women estimates that nearly 70% of Tunisian women are victims of abuse.
Amnesty International reported last year that there were few signs to show that things had improved for women since the Arab Spring revolution in 2010.