Kjær was included in the Denmark squads for the 1995 Intercontinental Cup, 1998 FIFA World Cup, Euro 2000 but he spent all three tournaments on the bench. He made his Denmark debut on 25 April 2001 in the farewell match of Peter Schmeichel. He was 35 years and 171 days old at the time, breaking the old record for oldest Danish debutant by 17 days, a record set by Johannes Gandil in 1908. He went on to play four international games until March 2002. He was included in the Danish squad for the 2002 FIFA World Cup, serving as a back-up to Thomas Sørensen.