Nørgaard won 73 caps and scored five goals for Denmark between U16 and U21 level. He was a part of the Danes' 2011 U17 World Cup and 2015 and 2017 European U21 Championship squads. Nørgaard was four times an unused substitute for the senior team during 2018–19 Nations League group stage and Euro 2020 qualifying matches in 2018 and 2019. On 8 September 2020, Nørgaard made his debut for the senior team with a start in a 0–0 Nations League draw with England and his performance was recognised with the DBU's man of the match award. After winning three further caps during the 2020–21 season, Nørgaard was named in the Denmark squad for Euro 2020. He appeared as a substitute in five of the six matches of the Danes' run to the semi-final.