Last November, the United Nations imposed sanctions against the ruling Taleban movement in Afghanistan.
Russian security sources are quoted as saying that the Boeing 727 will refuel there, before heading on "to a European capital, possibly London".
Up to 20 men - some armed with pistols, knives and grenades - are reported to have hijacked the plane during a domestic flight in Afghanistan on Sunday.
However, the Taleban movement in Afghanistan said it knew nothing of the demand.
Earlier, the plane landed in Tashkent, the capital of Uzbekistan, where 10 passengers - including women and children - were released, and the plane was refuelled.
It then flew to Aktyubinsk airport in northern Khazakstan - about 1,400km (875 miles) south-east of Moscow, where the hijackers are reported to have demanded food and fuel, before the plane took off again.
The plane is now at Moscow's Sheremetyevo 1 airport.
He is reported to have said that he was one of a group of hijackers opposed to the leadership of the Taleban movement.
Afghan dissident
The anti-Taleban alliance said it was not responsible for the hijack, and that an Afghan dissident called Gula Ajha was behind it.
They said he was on board the flight and had been in touch with the Uzbek authorities to demand that the aircraft be resupplied.
"We are not involved in this Ariana hijacking and condemn it," said Abdullah, spokesman for opposition leader Ahmad Shah Masood, who runs the 10% of Afghanistan outside the control of the Taleban movement.
Air traffic controllers lost contact with the plane early on Sunday as it left Kabul on its way to the northern city of Mazar-e-Sharif 40 minutes away.
It turned up after three hours at Tashkent airport, which was sealed off while the Ariana flight was surrounded by armed troops.
Relations poor
Correspondents say the arrival of the plane in Russia could cause complications.
The Taleban have recently recognised Chechnya as an independent state. Russia is currently trying to crush the rebel Chechen leadership, who the Taleban now recognize as the legitimate government.
Last November, the United Nations imposed sanctions against the ruling Taleban movement in Afghanistan.
The measures included a prohibition on international flights, though Ariana has continued to fly domestic routes.
Just over a month ago, the Taleban helped negotiate an end to a hijack when a plane from Indian Airlines was seized by pro-Kashmiri militants and forced to land in Afghanistan.
The Taleban were praised by the Indian Government and others for the way they helped secure a peaceful resolution.
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