Malmström began his career in the Swedish HockeyAllsvenskan, the country's second tier league, playing for his hometown team Kristianstads IK before moving to the Elitserien with Malmö Redhawks where he spent four seasons. He had a brief spell with HV71 in 2002 before returning to Malmö.
Malmström started his hockey career in the Swedish second-tier league, playing for his hometown team Kristianstads IK, before moving to the top tier Elitserien with Malmö Redhawks where he spent four seasons. He had a short stint with HV71 in 2002 before returning to Malmö.