Ingibjörg grew up in Grindavík in southwest Iceland and joined the local club Grindavík at a young age. On August 17, 2011, at 13 years old, she debuted for Grindavík's senior in a match against Þróttur Reykjavík in the top-tier women's football league in Iceland. In 2012, at the age of 14 years, Ingibjörg signed with Breiðablik, the record champions in Icelandic women's football. In August 2012, she debuted for Breiðablik senior team. Until 2016, she played alternately with the youth and senior team, then exclusively for the senior team.
