Mazur was born in Los Angeles, California, the daughter of Ruby Mazur, an illustrator known for creating the "tongue" logo for the Rolling Stones,[2] and her mother Valerie Chasin was a model. Mazur is the only daughter of four siblings. Mazur is of Jewish ancestry on her father's side.[3][4]
In the summer of 2005, Mazur gave birth to son Marlon, her first child, with husband, British film director Alex de Rakoff, whom she married in April 2005. In 2011, they had a second child, named Luciano Cy.[