Ingibjörg was born in Thingeyri, Iceland, in 1867 to Hakon Bjarnason and Johanna Kristin Þorleifsdóttir, and was one of five children. As a teenager, she moved to Reykjavík after her father died and attended Kvennaskólinn (the Reykjavík Women's College).[1] She graduated from the college in 1882 and relocated to Denmark to study gymnastics, making her the first Icelander to do so. She returned to the Reykjavík in 1893 to teach gymnastics at a children's school, and in 1903 she returned to the Women's College as a teacher.