Ahmed Newton Barry, commentator, former TV president, and ex-editor of L'Evenement newspaper, was targeted in an audio clip circulating among WhatsApp groups, the journalists' protection watchdog CPJ said late Thursday.
The speaker in the clip identifies Barry by name, describes him as a "terrorist" and says a hundred people would assault his home.
"We are going to set fire to it and then destroy everything and collect the rubble that is piled up and leave the ground vacant," the clip says, according to the CPJ.
Barry told the CPJ the threat may be related to comments he made on a TV program in which he described the Malian government as working with Russian mercenaries.
Angela Quintal, CPJ's Africa program coordinator in Johannesburg, urged the authorities to carry out a thorough investigation and ensure Barry's safety.
"The security of journalists in Burkina Faso is tenuous enough without their having to worry about a mob being provoked to attack their homes," she said.
Local press associations have also condemned the threats and urged the country's junta-dominated authorities to investigate.
One of the world's poorest countries, Burkina Faso is in the grip of a nearly seven-year-old crisis sparked by jihadist raiders crossing from neighboring Mali.
Thousands of people have been killed and nearly two million displaced.