A close ally of former President Blaise Compaore has been named the country’s new leader, state television reports.
The US, France and African Union (AU) 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.
A medical source in the city’s main hospital said three people had been killed.
An unknown number of protesters have been 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.
Mr Compaore was ousted in a popular uprising, partly organised by Balai Citoyen, in 2014 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.
In media interviews, he said he had no contact with Mr Compaore and would do everything to “avoid violence that could plunge the country into chaos”.
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 called for people to “immediately rise up” against the coup, and declared himself the leader of the West African state.
“We are in a resistance situation against adversity,” Mr Sy added.
The US State Department said it was deeply concerned about the events unfolding in Burkina Faso.
French President Francois Hollande said he strongly condemned the coup “because an electoral process was under way”.
However, France would not intervene militarily, he said.
The US said it was deeply concerned about events in Burkina Faso, and it condemned the seizure of power through unconstitutional means.
Burkina Faso is a key ally of the US and France in the campaign against militant Islamists in the region.