Malmström competed in the singles, doubles and mixed doubles events at the 1920 Summer Olympics. In the singles event he reached the quarterfinal after a bye in the first round and wins against Ladislav Žemla and Charles Simon. In the quarterfinal he was defeated by South African Louis Raymond. With compatriot Carl-Erik von Braun he lost in the first round of the doubles event against Jean Washer and Albert Lammens. In the mixed doubles event he teamed up with Lily Strömberg and after byes in the first and second round they lost the quarterfinal match against the Danish team Amory Hansen and Erik Tegner in three sets.