Sophie Petronin, who runs a non-governmental organisation that helps children suffering from malnutrition, was kidnapped on Saturday afternoon, but, so far, no one has made a claim of responsibility, Malian Commandant Baba Cissé said.
Mali has been beset by attacks from resurgent groups, including Al Qaeda in the Islamic Maghreb (AQIM) this year, especially in the north.
Gao - seized by militants in 2012 before French forces drove them out a year later - is considered the most secure town in northern Mali with multiple UN, French and Malian army checkpoints along main roads.
‘In liaison with the Malian authorities, they (French authorities) are fully mobilised to seek and release, as soon as possible, our compatriot,’ the French foreign ministry said.
A local radio station in Gao said the aid worker was affiliated with Aide Gao and was snatched by a group of men who drove off with her in a Toyota pickup truck.
Aide Gao was not available for comment.
Last month, despite the relatively heavy security in Gao, the offices of the UN peacekeeping mission located next to the city's airport terminal were razed by a truck-bomb explosion.
Mali's government signed a peace deal last year with secular armed groups, but militants pledging allegiance to both al-Qaeda and Islamic State have fought on and launched dozens of attacks on Western targets in recent months.
The peace agreement has been broken many times, adding to difficulties faced by UN forces trying to stabilise the former French colony.