Markov began his career in 1993, playing for HC Spartak Moscow in Russia. The Toronto Maple Leafs of the NHL drafted him in the 9th round of the 1995 NHL Entry Draft. However, partway through the 1996–97 season, he left Moscow and began playing for the Maple Leafs' farm team, the St. John's Maple Leafs. He made the jump to the NHL at the end of the 1997–98 season.