Minister of Communication Remis Dandjinou confirmed on Monday that the attack was over, with security forces carrying out checks on neighbouring buildings.
The shooting began shortly after 21:00 (21:00 GMT) on Sunday on Ouagadougou's busy Kwame Nkrumah Avenue.
Security forces launched a counter assault at 22:15 and the shooting ended at about 05:00 on Monday.
A Turkish restaurant, the Aziz Istanbul, popular with foreigners, appears to have been at the centre of the attack.
One eyewitness told the BBC: "I saw there were multiple trucks or jeeps driving through my street, with... local army/police officers with AK47s, deploying in front of my house.
"I heard a lot of shootings and then I was scared as hell and I went inside. I've been hearing quite a bit of shooting."
Police captain Guy Ye told Associated Press that the attackers had arrived on motorcycles and had begun shooting randomly.
Analysis: Alex Duval Smith, BBC News, Dakar
A terrorist attack in the Sahel had been expected.
Residents of Burkina Faso's capital had noticed more police road blocks in the past few days. In neighbouring central Mali, the United Nations mission, Minusma, had requested that staff and contractors avoid using rural roads.
Burkina Faso is part of the Sahel region, which includes Mali where Islamist groups have been active since 2012.
For nearly two years now northern Mali's terrorist challenge has grown into a regional problem, with attacks by al-Qaeda affiliates in Burkina Faso, Niger and Ivory Coast.
Even though the Ouagadougou attack was not prevented, the fact that Mali and Burkina Faso were on alert suggests Minusma's intelligence-gathering operation is bearing fruit.
France is spearheading fundraising for a regional anti-terror force, the G5 Sahel, which will draw from the armies of Mauritania, Chad, Burkina Faso, Mali and Niger.
The force will not be operational until later this year.
The Turkish and French governments confirmed that they had lost one national each in the assault.
French President Emmanuel Macron condemned the attack and said he would hold talks with his Burkinabe counterpart, Roch Marc Kabore, to "evaluate the situation".
The attack is similar to one in January 2016, when gunmen targeted the Splendid Hotel and the Cappuccino restaurant, only 200m further along Kwame Nkrumah Avenue from the scene of the latest attack.
More than 170 people were taken hostage and 30 were killed. The al-Qaeda in the Islamic Maghreb (AQIM) group said it had carried out that attack.
Under fire: Recent attacks in Burkina Faso
December 2016: 12 soldiers die in an attack by Islamist militants in the north, near the Mali border
January 2016: Islamist militants attack an Ouagadougou hotel popular with foreigners (above). Western nationals are among 30 people killed in the country's deadliest attack so far
March 2017: As the capital gears up for Fespaco film festival, two police posts in the north are attacked. Three people are killed
March 2017: Two people are kidnapped and a school is torched after jihadists threaten educational establishments