Markström has represented Sweden three times in junior tournaments. He backstopped the Swedes to a fourth-place finish in the IIHF World U18 Championships in 2008. The next year, he was placed on the Swedish World Juniors team and led all goaltenders with a .946 save percentage and finished second with a 1.61 GAA. Those impressive stats let him to earn Best Player honours at the goaltender position in 2009; his team also took home the silver medal. He again represented Sweden at the WJCs in 2010 and could not quite match his previous year's performance as Sweden earned a bronze medal. Markström did post a respectable .927 save percentage and a 2.21 GAA, both good enough for second place amongst goaltenders in the tournament.