Johansson was born in the Manhattan borough of New York City on November 22, 1984. Her father, Karsten Olaf Johansson, is a Danish architect who was born in Copenhagen. Ejner Johansson, her paternal grandpa, was an art historian, screenwriter, and film director whose father was Swedish. Melanie Sloan, a New Yorker, works as a producer; she hails from an Ashkenazi Jewish family from Poland and Russia with the surname Schlamberg, and Johansson identifies as Jewish.