Kvist was first called up on 17 August 2007 to the friendly match against Ireland on 22 August and has gone on to represent his country at European Championships and World Cups and is a firmly established member of the side.
Kvist was first called up to the Danish national team on 17 August 2007, for the friendly match against Ireland on 22 August. He has gone on to represent his country at European Championships and World Cups and is a firmly established member of the side.