Malmkvist has been a contestant in the Swedish Melodifestivalen, which is the qualifying contest for the Eurovision Song Contest, as well as at the European event, several times. She represented Sweden at the Eurovision Song Contest 1960 in London with "Alla andra får varann". In the following year Malmkvist sang "April, april" together with Gunnar Wiklund at that year's Melodifestivalen; the song won, and was performed by Barbro "Lill-Babs" Svensson as the Swedish representative at the international Contest, held in Cannes.