"In the night of 11-12 June, an operation of the Barkhane force allowed the capture of Oumeya Ould Albakaye, a senior figure in the Islamic State in the Greater Sahara (IS-GS)," a spokesman for the chief of staff told AFP.
The capture comes as France prepares to complete its withdrawal from Mali after almost a decade battling a jihadist insurgency in the country.
Albakaye will be held by French forces for questioning for several days and then handed to the Malian authorities, the military added.
A security source who asked not to be named told AFP that Albakaye had once been seen as a potential successor to former IS-GS leader Adnan Abu Walid al-Sahrawi, who was killed by French forces in August 2021.
An explosives expert, Albakaye was a regional chief in the group, commanding the areas of Gourma in Mali and Oudalan in neighbouring Burkina Faso.
He is responsible for a large number of abuses of civilians in those countries, the military said.
France is to complete its withdrawal from Mali within the next few months when its main military base at Gao will be returned to Malian forces.
Relations between Mali and France plummeted after the military seized power in Bamako in August 2020.
The junta has resisted setting an early date to restore civilian rule and tightened ties with Moscow, bringing in "military instructors" that France and its allies condemn as mercenaries hired from the pro-Kremlin Wagner group.