Kolkunov played one season with Krylja Sovetov of the Russian Superleague before being selected by the Pittsburgh Penguins 154th overall in the 1995 NHL Entry Draft. He would remain in Russia until the completion of the 1997-98 RSL season. On 13 July 1998, the Penguins signed Kolkunov to a three-year contract. Several months later, he attended camp with the Penguins but was later assigned to the Syracuse Crunch, who were the Penguins' AHL affiliate at the time. Kolkunov would remain in North America until the start of the 2000-01 ECHL season, where he chose to go home after eight games instead of continuing to play with the Wheeling Nailers. Kolkunov would finish the season with Ak Bars Kazan of the RSL.