A male HSBC vice president and senior product manager in New York says he was falsely accused of sexually harassing a female colleague and then fired because he is a man.

The March 27 sex discrimination lawsuit not only is one of the rare instances of sex bias allegations being brought by a man, it also comes with an added twist: Hussam Hariri says it was his female colleague who did the harassing.

The bank’s human resources department presumed Hariri...