Annika Olsen (born 13 March 1975, in Tórshavn, grew up in Vágur) is a Faroese politician, high school teacher and former swimmer. She was Deputy Prime Minister and Minister of Social Affairs in the Faroe Islands (2011–15) and Minister of Internal Affairs from 2008 to 2011 representing the People's Party (Faroe Islands). Before that she was a member of the from 2004 to 2008. Annika Olsen has an MA in Nordic languages and literature with a supplementary subject in religion. She is the daughter of Jákup Olsen, a businessman, former politician and former headmaster of Vágur's School and Marna Olsen, born Holm, a retired teacher.