Frostrup was born in Oslo, Norway, but moved with her family when she was six to Ireland in 1969, living in Kilmacanogue, a small village near the town of Greystones in County Wicklow. Her Norwegian father, an alcoholic who died aged 44 when she was 15, was a Journalist on The Irish Times, and her Scottish mother an Artist. She has four siblings, including a sister who was believed to be the incorrect age for a decade, until her birth certificate was discovered whilst moving house.