The attack on the army camp in Gourma-Rharous, about 120km east of Timbuktu, also destroyed a half-dozen vehicles, army spokesperson Lieutenant Colonel Diarran Kone said.
French air forces, alerted by Mali's army, responded as the assailants fled in two pick-ups, according to the Operation Barkhane statement. The town has been targeted regularly by Islamic extremists.
The recently formed extremist group Nusrat al-Islam wal Muslimeen claimed responsibility for an attack on Malian forces in Tagharost, about 150km south of Timbuktu, according to SITE Intelligence Group which monitors online extremist activities.
The extremist group said it staged a similar attack there, storming elite force barracks and taking vehicles.
Also on Tuesday, a United Nations peacekeeping mission vehicle was escorting a logistics convoy when it hit a land mine about 30km south of Tessalit in the Kidal region, the UN mission said.
Two peacekeepers and one civilian were wounded, it said. The Mali-based al-Qaeda affiliate Nusrat al-Islam wal Muslimeen claimed responsibility for the attack and for another one on UN forces in the Kidal region, according to the SITE Intelligence Group.
The extremist group said it destroyed two UN vehicles on the road between Aguelhok and Tessalit on Monday and hit the same convoy on Tuesday.
Ansar Dine, Al-Mourabitoun and al-Qaeda in the Islamic Maghreb in March declared they had merged into Nusrat al-Islam wal Muslimeen. A French-led intervention drove Islamic extremists from strongholds in northern Mali in 2013, but attacks continue.