The embassy attackers were armed with Kalashnikov assault rifles and were "dressed in civilian clothes" with their faces uncovered, witnessed said.
Rémi Dandjinou, Burkina Faso's minister of communication, told CNN on Friday that six attackers had been "neutralized" across the two sites.
The suspect in custody was arrested several hours after Friday's twin attacks on the French embassy and the country's military headquarters in the capital Ouagadougou saw seven soldiers killed, the source.
The landlocked nation of Burkina Faso is one of the poorest countries in the world.
French President Emmanuel Macron offered his condolences, Turkey's Recep Tayyip Erdogan, who is on a visit to neighbouring Mali, "strongly condemned" the attack while United Nations chief Antonio Guterres called for an "urgent and concerted effort" to improve stability in the Sahel. The victims were of several different nationalities.
An attack by gunmen a year ago on a restaurant in the capital left at least 18 people dead, including two attackers. They then ran towards the French embassy, according to witnesses who saw the attack from the state television offices facing the embassy. All eight militants were slain by security forces.
Al Qaeda in the Islamic Maghreb (AQIM) claimed responsibility for attacks on a restaurant and hotel in Ouagadougou in January 2016 in which 30 people were killed.
He further added that the attack might has been planned to target a meeting of the G5 Sahel which was underway in the military headquarters.
The 15 ambassadors expressed their solidarity with Burkina Faso in its fight against terrorism and also stressed the need to intensify regional and global efforts to combat terrorism and violent extremism, which may be conducive to terrorism. But experts say the terror threat in Burkina Faso is increasingly homegrown.
Burkina Faso like some of its West African neighbours has been targeted sporadically by extremist groups operating across Africa's Sahel region. In response to the new violence in eastern Burkina Faso, troops from Burkina Faso and nearby Mali and Niger have increased patrols.