The announcement was made on state television by an army officer, who said both the government and parliament had been dissolved.
Mr Kaboré’s whereabouts are unclear, but the officer said that all those detained were in a secure location.
The coup comes a day after troops seized barracks, and gunshots were heard in the capital.
Earlier, the ruling People’s Movement for Progress (PMP) party said that both Mr Kaboré and a government minister had survived an assassination attempt.
On Sunday, mutinying troops demanded the sacking of military chiefs and more resources to fight Islamist militants.
The army statement cited the worsening security situation and Mr Kabore’s alleged inability to unite the nation as reasons for overthrowing him, AFP news agency reports.
The statement was issued in the name of a group not heard of previously, the Patriotic Movement for Safeguard and Restoration or MPSR, its French acronym.
“MPSR, which includes all sections of the army, has decided to end President Kabore’s post today,” it said.