Two members of Burkina Faso's paramilitary gendarmes were killed defending the embassy, he said.
Ouagadougou has been attacked by Islamic extremists targeting foreigners at least twice in the past few years. Le Drian said the damage at the embassy was relatively minor.
"Stay indoors. Not clear at this stage which sites targetted", the embassy said in a second Facebook message.
"The security forces of Burkina Faso are mobilized against the attackers, with the support of the security forces of our embassy to reduce the threat", said the minister.
As per media reports, the witnesses heard gunfire before the blast and saw gunmen attacking the building. The defence minister said three assailants were killed at the army headquarters.
A government source said 16 people - nine assailants and seven members of the security forces - had died, a lot of them in the attack on the military headquarters.
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The US Embassy in Burkina Faso also warned US citizens to seek shelter amid reports of gunfire.
In a separate development on Friday, the specialist U.S. website SITE, which monitors jihadist activity, said kidnappers had released a video of a 75-year-old French hostage, Sophie Petronin, who had been abducted in northern Mali in late 2016.
Smoke rises from the site of an attack in downtown Ouagadougou, Burkina Faso March 2, 2018.
The ministry's website recommended that people stay off the streets and remain in a safe place.
Although soldiers and police officers are reported to be among the wounded no civilian casualties have been so far been reported.
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Witnesses said five armed men got out of a vehicle and opened fire on passersby before heading towards the French embassy.
A Reuters reporter saw an ambulance entering the army compound.
Burkina Faso's national police warned people to move away from areas around the "vicinity of the Prime Ministry - and the United Nations roundabout" in a post on its Facebook page.
Witnesses at state TV offices that face the embassy told The Associated Press that five attackers arrived in a pickup truck, shouted, "Allahu Akhbar", and began shooting. They said the attackers left the truck, set fire to the embassy and started shooting.
Suspected jihadists killed at least 18 people last August during a raid on a restaurant in Ouagadougou, and terrorists have targeted Burkinabe security forces along its remote northern border region with Mali.
Joel Embiid and Lebron James #summer2018goals
For now, The King and his Cavaliers will have to take that L for another 35 days until both of these teams meet again. The 76ers held on from there to produce their first win after losses to Washington and Miami .