Songwriter Andy Stone says he co-wrote a song with the same name five years earlier, arguing that Ms Carey exploited his "popularity" and "style".
Despite sharing a title, the two songs appear musically different, but Mr Stone claims Ms Carey caused confusion and did not ask for permission.
Ms Carey has not yet responded.
A must-have on any Christmas playlist, Mariah Carey's All I Want for Christmas is You is one of the best known Christmas records of all time.
