Klaassen made his debut for the Dutch national team at youth levels, debuting for the Netherlands U-16 team on 28 October 2008 in the 10th edition of the Tournoi Val de Marne '08 in the 3–0 victory over Italy U-16, while scoring the second goal for the Netherlands in his first international encounter. Klaassen scored in his second appearance for the Netherlands U-16 in the same tournament as well in 0–1 win over France U-16. In total Klaassen made 5 appearances for the Netherlands U-16 while scoring 4 goals. Scoring two more goals in friendly encounters against Ukraine U-16 and Ireland U-16 as well. On 22 September 2009, Klaassen made his first appearance for the Netherlands U17 team in a friendly encounter against France U17 which ended in a 1–0 loss for the Dutch. On 3 March 2010, he scored his first goal for the under-17 side in his 8th appearance, a friendly match against Greece U17. He also played a major role in the Netherlands qualifying campaign ahead of the 2010 UEFA European Under-17 Football Championship as well as playing in the 2009 edition of La Manga Cup. On 2 September 2010, Klaassen made his debut for the Netherlands U19 team in a friendly match against Germany U19 which ended in a 2–2 draw. In his 7th appearance for the under-19 side he scored both his first and second goal on 10 November 2011 in a qualification match ahead of the 2012 UEFA European Under-19 Championship against Moldova U19 with the Netherlands failing to qualify for the final tournament in Estonia.