At the age of 14, Ingibjörg was called for the Icelandic U-17 team, which participated in the qualifying tournament for the 2012 UEFA Women's Under-17 Championship. Her first game for the U17 team was on April 18, 2012, in Poperinge against Belgium. Ingibjörg also participated in the qualifying tournament for the 2014 UEFA Women's Under-17 Championship. In March 2014, Ingibjörg debuted for the Icelandic U-19 team in a match against Finland. Ingibjörg played her first international match for Iceland senior team on June 8, 2017, in a 0–0 away game against Ireland when she played 90 minutes. Shortly thereafter, Ingibjörg was included in the squad that represented Iceland at the UEFA Women's Euro 2017. She played against France and Switzerland in the Group Stage.