The video has been shown at other concerts on the singer's tour, and the party has expressed its outrage before, warning that it would take action if the video were shown in France. On Saturday night, Madonna played it at the Stade de France.
National Front spokesman Alain Vizier said Sunday that the party would file a complaint in French court next week for "insults."
Party leader Marine Le Pen is briefly pictured in the video during a montage in which famous faces - or parts of faces - morph one into the next. Soon after Le Pen's face flashes up, Madonna's face follows with Hitler's mustache.
Le Pen, who inherited control of the party from her father, Jean-Marie, has tried to shed the National Front's image as racist and anti-Semitic, especially during her recent failed bid for president. But she has maintained a hard line on immigrants, saying France has too many and criticizing many Muslims, in particular, for insufficiently assimilating into French culture.
Meanwhile, anti-racism group SOS Racisme expressed its support for Madonna on Sunday, commending her for her "resolutely anti-racist and feminist discourse."