Beatrice Stockly was taken from her home in Timbuktu with the video demanding a jihadi be released in exchange for the nun.
The shocking eight-minute clip sees Stockly dressed in a hijab in front of an al-Qaeda banner draped in slogans.
She outlines the conditions that would see her released including the freeing of extremist Ahmad Al Faqi Al Mahdi.
Al Mahdi is currently in custody at the International Criminal Court.
Ms Stockly claims in the video that it was filmed on January 19 with an English-speaking jihadi saying the nun was abducted for teaching Christianity.
The capture comes four years after she was abducted by militants from her home and al-Qaeda in the Islamic Maghreb (AQIM) have taken responsibility.
The fighter says al-Qaeda carried out the abduction and took the nun because she "drove out many from the fold of Islam by seducing them with crumbs of this worldly life".
Timbuktu town councillor Bilal Mahamane Traore added: "People were sleeping but neighbors heard the noise — the woman screamed a lot".
Army spokesman Souleymane Maiga said the woman was "kidnapped at 3.30am" from her Timbuktu home.
He added: "A neighbour alerted the security forces around 6am."
Al-Qaeda claimed responsibility for an attack on a Bamako hotel where 20 were killed in November last year.
It is the first abduction in northern Mali since November 2013 when two French journalists were abducted and killed.
Stockly was taken hostage in 2012 but was released just days later and returned to work as a missionary.
