A witness at the scene told Reuters that masked gunmen with backpacks attacked the army headquarters after the explosion.
Police took up positions near the offices of the prime minister where gunfire was also reported.
Previous attacks were conducted by allies of al Qaeda in reprisal for Burkina Faso's participation in a regional fight against Islamist militants.
About 30 people were feared killed after suspected Salafi jihadists launched a three-pronged assault on public offices across the Burkinabe capital, local media reports said Friday.
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. At least seven attackers were said to have been killed in shootouts with the troops. Guterres is closely watching and following the events and asked the special representative for West Africa and the Sahel, Mohammed Ibn Chambas, to travel to Burkina Faso as soon as possible.
Witnesses said that men with guns got out of the auto and opened fire on the buildings. The authorities think both attacks were made by terrorist group Boko Haram.
Barricades were erected to keep people from that area and from the French Embassy and the prime minister's office in the eastern part of the city center where gunfire and smoke were reported.
Eight members of the armed forces were killed by the blast and the parallel attack on the French embassy, while 80 were wounded, said Security Minister Clement Sawadogo.
But the French embassy themselves have come out to say they are not being targeted.
No group has claimed responsibility although suspicion will fall on a disparate group of Islamist movement active in the West African region.
The country had earlier contributed troops to join about 4,000 French troops who had been battling insurgents in the Sahel region on the southern rim of the Sahara.
Five countries - Burkina Faso, Niger, Chad, Mali and Mauritania - launched a new task force previous year to tackle Islamist militants in the arid Sahel region, to which global donors have committed $500 million US.