 Slovak played as a youth in the developmental program of hometown club, HC Košice, from 1997 to 2001.He made his Slovak Extraliga debut with Košice in the 1999–00 season, appearing in a pair of games.After impressing on the international junior stage for the Slovak junior team, Slovak was selected by the Nashville Predators in the second round, 42nd overall, in the 2001 NHL Entry Draft.