Radio Omega was immediately suspended on Thursday "until further notice," Communications Minister Rimtalba Jean Emmanuel Ouedraogo said in a statement.
He said the measure was "in the higher interests of the Nation."
The station, part of the Omega media group owned by journalist and former foreign minister Alpha Barry, ceased broadcasting after the statement was issued late Thursday.
The channel had run an interview with Ousmane Abdoul Moumouni, the spokesman of a newly-established Nigerien group campaigning to return President Mohamed Bazoum to power.
The country's elected leader was overthrown on July 26 by members of the Presidential Guard.
Moumouni made "insulting comments with regard to the new Nigerien authorities," said Ouedraogo, who is also government spokesman.
His organization "is clearly campaigning for violence and war against the sovereign people of Niger" and seeks to restore Bazoum "by every means," he charged.
Radio Omega on Friday said it would turn to "every means of recourse" to fight the suspension.
The decision is a "blatant violation of current laws and an unacceptable attack on freedom of expression and freedom of the press," it said.
The order, it added, came after "numerous death threats" had been made against the station's managers and journalists "from people describing themselves as supporters of the government."
Burkina Faso underwent two military coups last year, each triggered in part — as in Mali and Niger — by discontent at failures to stem a raging jihadist insurgency.
It swiftly declared solidarity with Niger's new leaders and joined Mali in warning that any military intervention to restore Bazoum would be considered a "declaration of war" against them.
The Burkinabe authorities in recent months have suspended the French TV outlets LCI and France24 as well as Radio France Internationale, RFI, and expelled the correspondents of the French newspapers Liberation and Le Monde.