The jihadist group is responsible for the deaths of thousands of civilians and officials in the African country.
Earlier this month, France 24 held an on-air discussion about an exclusive interview they conducted with the Algerian Abu Obeida Youssef al-Aanabi, the leader of the group al-Qaeda in the Islamic Maghreb (AQIM).
Wassim Nasr, the journalist who did the interview, told the Associated Press news agency that the TV station had decided not to broadcast it.
What did the government say?
Burkina Faso's communication minister, Jean-Emmanuel Ouedraogo, said that by interviewing the head of the Islamist group, "France 24 is not only acting as a mouthpiece for these terrorists but worse, it is providing a space for the legitimization of terrorist actions and hate speech."
"The government is disheartened to see that the head of a terrorist organization like AQIM and recognized as such by the entire international community can take advantage of the editorial generosity of France 24 to talk at length on the channel's airwaves," Burkina Faso's military junta said in a statement.
How did France 24 respond?
France 24 denounced the government's accusations as "outrageous and defamatory."
"The management of France 24 condemns this decision and disputes the baseless accusations calling into question the channel's professionalism," the news station said.
In December, Radio France Internationale (RFI) was also suspended on accusations of sending a "message of intimidation" attributed to a "terrorist chief."
RFI and France 24 have also been suspended in Burkina Faso's neighbor — Mali, which is also under military rule fighting against the Islamist insurgents.
"The security crisis the country [Burkina Faso] is going through must not be a pretext for muzzling the media," France 24 said.
What is the situation in Burkina Faso?
Islamist militants linked to al-Qaeda and the so-called "Islamic State" groups have been waging a fierce insurgency in one of the world's poorest countries for seven years.
Thousands have been killed, and nearly 2 million people have been displaced due to this rebellion.
Last year, Burkina Faso saw two military coups amid instability caused by the terrorist groups that control about 40% of the country, according to official figures.
France, the former colonial power in the African region, also withdrew its troops last year from Mali, Burkina Faso and the Central African Republic. The soldiers were supporting the Sahel Nations in fighting the insurgents.
Junta leader Captain Ibrahim Traore vowed to regain control after coming to power in September.
aa/fb (AFP, AP, Reuters)