Sigríður Lára represented Iceland at the 2011 UEFA Women's Under-17 Championship, where Iceland finished fourth. She also represented her country in the qualifyings for the 2012 UEFA Women's Under-19 Championship and 2013 UEFA Women's Under-19 Championship. In both occasions, Iceland failed to qualify. Sigríður Lára debuted for the Icelandic senior team on February 14, 2016, in a 1–1 tie against Poland. She also played for her country at the 2017 Algarve Cup. On June 22, 2017, Sigríður Lára was included by coach Freyr Alexandersson in the squad that represented Iceland at the UEFA Women's Euro 2017. She played two matches in the tournament, against France and Switzerland.
