Russian media reports identified the man as Shamil Abidov, who was wanted for a series of attacks on security forces over the past three years.
Abidov was said to be a close associate of Rasul Makarsharipov, the leader of an armed militant group. Makarsharipov was killed in the regional capital Makhachkala in June last year.
The security operation began on 13 January when a group of militants was spotted in the Sergokala district. One other militant was also killed and a special policeman wounded.