"One fighter was killed on 2 February during an operation carried out by federal special forces in the Chechen republic," Russian news agencies quoted the Kremlin press office as saying on Thursday.
The dead fighter held a Turkish passport bearing the name of Ziya Pece. A grenade launcher and a gun were found near his body.
At least seven Turkish fighters were killed by Russian forces in Chechnya last year.
The latest killing prompted a senior Russian defence ministry official to renew criticism of Turkey for failing to prevent its nationals from infiltrating Chechnya and fighting on the separatists' side.
"We keep killing armed Turkish citizens on Chechen territory," the official said.
"Turkey, which is a NATO member, is not taking the necessary steps to prevent fighters from infiltrating Russia, which is itself a partner of NATO and an active member of the international anti-terrorist coalition," he added.
Moscow last month upbraided Turkey for failing to act decisively against organisations and individuals who have provided backing to Chechen fighters.
Russia, which sent troops into Chechnya in October 1999 to put down a separatist insurgency, has frequently complained that the fighters have received backing from citizens of Muslim states, in particular Saudi Arabia.