Mr Kadyrov, who is Chechnya's deputy prime minister, condemned Danish aid groups, late Monday, over the publication that has sparked a wave of protest around the globe.
He had decided, he told Russian media, "not to allow into Chechnya anything that comes from Denmark".
"They play on the feelings of 1.5 billion people, acting as provocateurs... Danish social organisations and everything that comes from there will be banned," Mr Kadyrov said.
But the Russian Kommersant newspaper cast doubt on the legality of the move by Mr Kadyrov, who at 29 is seen as Chechnya's de facto head and likely to take on the role of his father, a Chechen leader killed in a bomb attack in 2004.
The Danish organisation that could be most missed is the Danish Refugee Council, which has provided food and shelter to Chechens through two wars and continued lower-level violence, the Kommersant said.
The head of the council's international branch, Arne Vaagen, said that the group was cutting back activities in Chechnya and neighbouring Dagestan after being told "by the United Nations that the Chechen deputy prime minister no longer wants Danish workers in the region".
The Danish Refugee Council (Dansk Flytningehjaelp) has already closed two offices in Sudan's troubled Darfur region after attacks by demonstrators protesting at the cartoons.