The suspect is being held in Maikop, capital of the Adygeya Republic in southern Russia.
An unidentified Interior Ministry official says the student is suspected of uploading the video to the Internet, but is not its creator.
The video shows two men with their mouths gagged and their hands tied behind their backs, kneeling in a forest in front of a large swastika flag. The film then shows a masked man beheading one man with a hunting knife.
Another section of the video shows a man shouting "Glory to Russia," before shooting the second captive in the head.
A caption on the video identifies one victim as being from Daghestan and the other from Tajikistan.
Another caption says the video is the work of a group calling itself the National Socialist Party of Rus.
(Interfax, Reuters, AFP)