The militant, detained on Tuesday, is believed to have been a member of the Arsayev militant group during December 1999 - April 2000.
The four men, detained in the republic's southern district of Vedeno and the Nozhai-Yurt district in eastern Chechnya, allegedly supplied Chechen militant groups with food and other supplies.
Police also seized and destroyed a home-made explosive device in the Vedeno district.
In a separate development, police in the North Caucasus republics of Daghestan and North Ossetia, uncovered two arms caches.
In North Ossetia, which borders Chechnya in the northeast, police seized an RPG-26 grenade launcher, 13 grenade launcher rounds, three hand grenades, over 500 cartridges as well as a small amount of explosives.
Police in Daghestan's Khasavyurt district confiscated seven grenade launcher rounds, eight hand grenades, over 1,000 cartridges, as well as food and medicine.