At least five people were killed and two attackers "neutralized" there, he said.
The West, particularly France, considers Burkina Faso a key ally in the fight against al Qaeda in the region.
Five emergency centers were set up in hospitals, a military barracks and at a stadium in Ouagadougou to treat the casualties, said Col. Amade Kafando, director general of Burkina Faso's army health department.
French Foreign Minister Jean-Yves Le Drian also said the assault was most probably carried out by "terrorist groups".
An emergency medical post was established at the municipal stadium.
The national police said in a statement that eight gunmen were killed: four at the embassy and four at the army headquarters.
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"The attack concerns the following areas according to the first information available: around the Prime Ministry, the roundabout near United Nations", it said.
"I saw people with sacks on their backs attack the guard".
Though gunfire and explosions have been heard, no casualty has been reported thus far. "I saw soldiers flee the army headquarters building running", witness Kader Sanou told Reuters. An explosion rocked the compound, setting the building on fire and sending up a thick column of black smoke.
Panicked residents fled the city centre on foot or motorbikes as dozens of Burkina Faso soldiers and armoured vehicles took up positions in the area.
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Investigators have also arrested 13 people, including some high-ranking bank officials, for their alleged involvement in the fraud.
Heavy smoke was seen coming from the army joint chief of staff's office in Ouagadougou. Avoid downtown Ouagadougou. Shelter in place. The two targets are a few meters away from the prime minister's office in the city.
Burkina Faso's communications minister says four Islamic extremists have been killed after they attacked the French Embassy in Ouagadougou, the capital.
The embassy initially said on its Facebook page that an attack was underway at the embassy as well as Ouagadougou's French cultural institute.
It ceased by around noon.
France's ambassador to Burkina Faso, Xavier Lapdecab, urged people via Twitter to act with "absolute precaution" as the attack is ongoing.
In Paris, President Emmanuel Macron's office said the French leader was "being informed in real time" of the situation.
Burkina Faso is a former French colony and, like several others countries in west and central Africa, retains close security and trade links with Paris.
The landlocked nation of Burkina Faso is one of the poorest countries in the world.
Macron was being kept up to date with events in Ouagadougou, the Elysee Palace said in a statement.
There were conflicting reports over the number of deaths however, AFP news agency reported that at least 30 people were killed in the attack.