A close ally of former President Blaise Compaore has been named the country’s new leader, state television reports.
French President Francois Hollande condemned the coup in the former French colony.
Those killed were shot dead by presidential guard forces in the capital, a civil society group said.
The claim by the influential Balai Citoyen group could not be independently verified.
Other reports said protesters had been assaulted and detained.
The coup leaders have imposed a night-time curfew across the West African state, and have ordered the closure of land and air borders, AFP news agency reports.
The headquarters of Mr Compaore’s Congress for Democracy and Progress (CDP) party were ransacked in Ouagadougou as news of the coup spread, it adds.
Mr Hollande called for the immediate release of interim President Michel Kafando and Prime Minister Isaac Zida, who were detained at a cabinet meeting in the president palace on Wednesday.
Their transitional authority was due to hand power to a new government after elections on 11 October.
It is one of the world’s poorest countries – its main export is cotton
A former French colony, it gained independence as Upper Volta in 1960
Capt Thomas Sankara seized power in 1983 and adopted radical left-wing policies – he is often referred to as “Africa’s Che Guevara”
The anti-imperialist revolutionary renamed the country Burkina Faso, which translates as “land of honest men”
Mr Compaore took power in the coup that killed Mr Sankara, and ruled for 27 years, until he was ousted last year following street protests
People in Burkina Faso, known as Burkinabes, love riding motor scooters
It is renowned for its pan-African film festival, Fespaco, held every two years in Ouagadougou
Mr Compaore was ousted in a popular uprising last year after 27 years in power, and is currently in exile.
He was accused of committing widespread abuses, and trying to change the constitution to extend his term in office.
Some of his key allies had been barred from contesting the election.
A statement issued by the coup leaders said the West African state would be led by Gen Gilbert Diendere, Mr Compaore’s former chief-of-staff.
An earlier announcement on state television said wide-ranging talks would be held to form a new interim government that would organise “peaceful and inclusive elections”.
Transitional parliamentary speaker Cheriff Sy said the move was “clearly a coup”.
He said the presidential guard had “sequestrated” the interim government, and he urged people to protest on the streets.
“We are in a resistance situation against adversity,” My Sy added.
The elite presidential guard has been trained, in part, by the US. It is the most powerful armed group in Burkina Faso and often disrupted the activities of the transitional government as it tried to cling to the privileges it enjoyed under Mr Compaore’s rule.
It is seen to be close to him, and is not popular on the streets. So its seizure of power could be a recipe for serious violence.
The transitional government might have made two mistakes – preventing politicians loyal to Mr Compaore from running in next month’s elections and allowing the Reconciliation Commission, formed to heal wounds after the end of his authoritarian rule, to release a report calling for the presidential guard to be disbanded.
Some argue that a newly elected president would have had greater legitimacy to take such action.