A hand grenade was thrown at French soldiers shortly after the arrival of President Emmanuel Macron on an official visit to the African country.
He played down the reports of the attack, saying much worse assaults linked to "deadly … terrorism" targeted the country.
Eyewitnesses said two people on a motorcycle threw the grenade late Monday in a neighborhood of the capital, Ouagadougou. The assailants missed their intended target — a bus carrying members of the French military.
Three civilians were injured in the attack, just hours before Macron was due to speak before a university audience at Ouagadougou, RFI radio station said.
"Let's put things in perspectives and keep our cool," Macron said in a news conference at Burkina Faso's presidential palace.
"It's only a grenade, I don't forget the deaths your people had to suffer yesterday, and in the weeks and months before," he said, adding: "And they are victims of what? Not to a reaction to a visit by France's President. They are the victims of terrorism, of the deadly obscurantist terrorism against which we
are all fighting with determination."
Later, on Tuesday, stones were thrown at one of the vehicles that were part of the French delegation, Macron's spokesman said, adding that the French president was not in that car but speaking with Burkino Faso's president, Roch Marc Kabore.
Macron and German Chancellor Angela Merkel are due to address a European Union-Africa summit in Abidjan this week, focusing on education, investment in youth and economic development to prevent refugees and economic migrants from attempting the treacherous journey across the Mediterranean.
Burkina Faso has been battling a surge in violence blamed on extremists. The violence has included two attacks on restaurants popular with foreigners, including one in August that killed 18 people.
Macron landed late Monday in West Africa, where he is expected to try to revive French influence and move beyond post-colonial tensions despite threats of demonstrations.
In his first big speech on Africa, the 39-year-old leader is expected to focus on more pragmatic relations, such as supporting startup entrepreneurs instead of giving aid.
The Burkina government has ordered schools closed to ease traffic because of the heavy security measures in place during Macron's visit, though many view the closures as an effort to reduce the threat of student unrest.
Unions in Burkina Faso already have called for protests against Macron's visit to Ouagadougou ahead of the Europe-Africa summit in the Ivory Coast. Macron also will make a stop in Ghana after attending the summit in Ivory Coast.
Burkina Faso, a former French colony, is now part of a five-country regional security force aimed at eliminating extremists in the Sahel.
Long a country of relative peace, Burkina Faso has seen the threat of extremists spill over the border from neighboring Mali in recent years.
On Sunday, a teacher of French and geography was killed in Burkina Faso's Yatenga province near the Malian border. Authorities have called it a "terrorist attack," and said two others were wounded.