Pääjärvi made his international debut for Sweden at age 14 with the under-16 team during the 2005–06 season; the following season, he became the scoring leader for the U16s. During the 2008 World Junior Ice Hockey Championships in Pardubice and Liberec, Czech Republic, at 16 years and eight months old, he became the youngest player ever to play for Sweden during a World Junior Hockey Championship. During the tournament, he scored one goal, and helped Sweden to the finals when assisting Mikael Backlund on Sweden's overtime game-winning goal against Russia in the semifinal.