Annika Olsen (born 13 March 1975, in Tórshavn, grew up in Vágur) and 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 City Council of Tórshavn 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.
At the general election 2015, the People's Party lost two seats in the Faroese parliament, they got 18.9% of the votes and 6 members. Annika Olsen got second most votes of the parties candidates. Eight days after the election, Olsen who had received 961 personal votes, left the People's Party, which means that the party lost one member and now has 5 parliament members. On 17 September she joined the Liberal party Progress, which is part of the governing coalition. She was subsequently elected as chairman of the Fiscal committee. Three days later, she regret her decision and left Progress and also said she would not be the chairman of the Fiscal committee. She needed some time alone with her family and took leave from the parliament. She asked the people who elected her to forgive her, she had had too little time to think before she joined another party.
On 4 February 2016 she became a member of the People's Party again.
Between 1988 and 1995 Annika Olsen was a member of the Faroese national swimming team. She attended the Island Games in 1991 and won a bronze medal in 200 m breast, bronze in 4x50 m free, bronze in 4x100 m free and silver in 8x50 m free. She also attended the Island Games 1989 in the Faroe Islands.