Naslund began his career in Sweden, playing for Team Modo Hockey. Naslund was still quite young at that time. He played very well and was drafted by the NHL. In 1994, after being drafted by the NHL, he was taken in by the Pittsburgh Penguins. He started his rookie NHL years here. He did not play many games as he was not seen to be a great player at that time. Finally, the manager of the Penguins traded him to the Vancouver Canucks.