Police stormed into an apartment sheltering suspected fighters "who seeped into Dagestan from Chechnya and planned a series of terrorist acts, including capture of hostages and vitally important objects", officials were quoted by the Russian Interfax news agency as saying.
Police also said they detained a suspected accomplice.
Dagestan is a mostly Muslim republic that saw a series of incursions from Chechen rebels in 1999, as the separatists tried to establish an Islamic state on Russia's volatile southern border.
Armed separatist groups have been fighting pro-Moscow forces in Chechnya for most of the past decade.
The current war began in October 1999 as an intended quick Russian military operation that was unexpectedly met by stiff Chechen resistance.
It has since dissolved into a guerrilla war that continues to claim lives on both sides of the conflict on a nearly daily basis.