There have been airstrikes in recent days in the surrounding mountains where Islamist insurgents are believed to be hiding in hillside caves.
"The French are controlling the airport with the back-up of two paratrooper units," a ministry official said, adding that nearly 4,000 French troops were now on the ground in Mali.
The official said French air strikes had hit 25 targets in recent days, "mainly logistical depots and training centres" in the areas of Aguelhok and Tessalit, near the Algerian border.
French-led forces have driven out the fighters who had controlled the north for 10 months, from their key strongholds in Gao, Timbuktu and Kidal.
The rebels melted away into the Adrar des Ifoghas massif around Kidal, where they are believed to be holding seven French hostages kidnapped in Mali and Niger in 2011 and 2012.
Dozens of French warplanes have carried out air strikes in recent days on rebel training and logistics centres in the region, near the Algerian border and some 1,500 kilometres northeast of Bamako.
Foreign Minister Laurent Fabius said on Monday the strikes were aimed at blocking the rebels' supply routes to flush them out.
Some 600 French troops based in the city of Timbuktu prepared to withdraw on Tuesday, crossing the Niger River and making their way to Gao before heading to Kidal, according to a military source.
On Monday Fabius said France was working to "very quickly" withdraw its forces from Timbuktu and hand the baton over to African troops.