She first became involved in the women's suffrage movement in Iceland in 1894. In 1915, when Icelandic women won the right to vote, Ingibjörg was chosen by a women's organisation to address parliament and present a celebratory speech, and was elected the head of a committee which raised funds to build a hospital, Landspítali (the National University Hospital) to commemorate the suffragists' win.[2] She led the Women's Slate, a precursor to the feminist Women's List political party, and in 1922 was elected to the Althing.[1][2] She thereby became the first woman to sit in the Icelandic parliament.[1] She initially ran as an independent member, but in 1924 she joined the Conservative Party and stayed in office as a Conservative member until 1927. In her political career, she promoted women's and children's rights, although she never married or had children.[2]