Around two kilometers (1.24 miles) away the French embassy also came under attack after a van sought to break through the buildings' barrier.
"Four attackers were neutralised in the attack on the French embassy", it said in a statement posted on its Information Service website.
Inhabitants of Ouagadougou are still to recover from shock after militants carried out simultaneous attacks on Friday morning on the military headquarters of Burkina Faso and the French Embassy in Ouagadougou.
At the same time, the bomb went off near the headquarters of the Burkinabe armed forces and the French cultural centre, about a kilometre (half a mile) from the site of the first attack, other witnesses said.
Previous extremist attacks had been on soft targets of restaurants which caused a greater loss of civilian lives. Witness said loud explosions were still heard around the army headquarters.
Five regional countries launched a new taskforce in 2017 to tackle Islamist militants in the zone, to which global donors have committed a half-billion dollars.
In a phone call to President Roch Marc Christian Kaboré, the Secretary-General expressed solidarity with the Government and people of Burkina Faso. Attacks have spread into Burkina Faso, and a local extremist group has also gained momentum, attacking troops and civilians. There was no claim of responsibility.
People on Saturday flocked around the headquarters and the French Embassy to view the damage.
Although a government source said 16 attackers and defenders died, the AFP learned unofficially that the attacks may have been bloodier than the official narrative, which earlier in the day had only admitted the deaths of four of the attackers.
Following the latest attacks, Taiwan's Deputy Foreign Minister Wu Chih-chung contacted Burkina Faso's Ambassador to Taiwan Aminata Sana Congo to convey the condolences of President Tsai Ing-wen and the Taiwanese people, MOFA said. We saw that they had set a vehicle on fire.
In August, extremists opened fire as patrons dined at a restaurant, killing at least 18 people.
A military barrier is placed along a street leading to Burkina Faso's army headquarters in the capital Ougadougou, Burkina Faso.
"Nothing, absolutely nothing, can justify such indiscriminate fury against the Burkinabe state, its institutions and the fearless people who love peace, democracy, justice and progress", he said.