At age 15, Näslund played a season with Örnsköldsviks SK in Sweden's third-tier men's league. Appearing in 14 games, he scored 7 goals and 13 points. The following season, in 1989–90, Näslund joined the Modo Hockey organization, playing in Sweden's highest-level junior league, the J20 SuperElit, where he and Peter Forsberg skated together on one of the most productive lines in the league. The pair helped Modo to win back-to-back junior championships. After a season of junior, in 1990–91 Näslund joined Modo's professional team in the Elitserien, Sweden's premiere league. The Modo equipment manager designated him with the jersey number 19, which Näslund thereafter opted to wear with the Swedish national teams he played on. He recorded 10 goals and 19 points in his rookie season, a record points total for a 17-year-old in the league, until Robert Nilsson scored 21 in 2002–03.