The video appeared to show a masked man hacking off the head of one captive with a knife.
In another section, a man could be heard shouting "Glory to Russia", then firing a hand gun at the head of the second captive, who was kneeling next to a shallow grave.
A Russian interior ministry spokesman said: "We have detained a young person suspected of uploading this video to the Internet. This man has declared his devotion to national socialist ideas."
The student was held by police in the town of Maikop, the capital of the Adygeya region in the south of Russia.
The spokesman said: "According to preliminary information, he has been distributing this video over the internet but he is not the author of it ... Experts are still working to establish the authenticity of the video."
Svetlana Gannushkina, a human rights campaigner, said she had seen the video and believed it showed genuine executions.
She also said she had "looked through the [web]site they referred to in this video and unfortunately, there were mainly positive comments on it" regarding the video.
A caption on the video said it was the work of the Rus National-Socialist Party, a previously unheard of group.
"Rus" is a historical name for Russia and has been used by nationalists.
Vladimir Putin, the Russian president, has condemned racism, but a report last year by Amnesty International, the rights group, said violent racism was out of control in Russia and there has been increasing number of attack against migrants.
Since the break-up of Soviet rule, millions of migrants, mainly from the country's south or former Soviet republics, have travelled to Russia to find work.