Heavy arms fire at the capital Ouagadougou's Sangoule Lamizana camp, which houses the army's general staff and a prison whose inmates include soldiers involved in a failed 2015 coup attempt, began at least as early as 5am (1600 AEDT) on Sunday, a Reuters reporter said.
The reporter later saw soldiers firing into the air in the camp, and the air base close to Ouagadougou airport. A witness also reported gunfire at a military camp in Kaya, around 100 kilometres north of Ouagadougou.
Burkina Faso's government confirmed gunfire at some military camps but denied reports on social media that the army had seized power.
Speaking on national television, Defence Minister General Bathelemy Simpore denied rumours that President Roch Marc Kabore had been detained, adding the motive behind the gunfire was still unclear.
"The head of state has not been detained; no institution of the country has been threatened," Simpore said.
"For now, we don't know their motives or what they are demanding. We are trying to get in contact with them," he said, adding that calm had returned to some of the barracks.
Governments in West and Central Africa are on high alert for coups after successful putsches over the past 18 months in Mali and Guinea.
The military also took over in Chad last year after President Idriss Deby died on the battlefield.
Burkinabe authorities arrested a dozen soldiers earlier this month on suspicion of conspiring against the government.
The arrests followed a shake-up within the army's leadership in December, which some analysts saw as an effort by Kabore to shore up his support within the military.
Rising violence in the West African country by Islamist militants linked to al Qaeda and Islamic State killed more than 2000 people last year, prompting violent street protests in November calling for Kabore to step down.
Additional demonstrations were planned for Saturday, but the government banned them and the police intervened to disperse the hundreds of people who tried to assemble in Ouagadougou.
The government has suspended mobile internet service on several occasions, and the tense situation in November led the UN special envoy to West Africa to warn against any military takeover.
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