The company said it filed the lawsuit last week after the Beastie Boys threatened their own legal action for copyright infringement.
"GoldieBlox created its parody video specifically to comment on the Beastie Boys song, and to further the company's goal to break down gender stereotypes and to encourage young girls to engage in activities that challenge their intellect, particularly in the fields of science, technology, engineering and math," the company's lawsuit stated.
On Monday, the two surviving band members - Adam Horovitz and Michael Diamond - said in an "open letter" that they support the company's message of empowering girls.
But they have a blanket ban on using their songs in advertisements.
"As creative as it is, make no mistake, your video is an advertisement that is designed to sell a product, and long ago, we made a conscious decision not to permit our music and/or name to be used in product ads," the band members said through their publicist.
"When we tried to simply ask how and why our song Girls had been used in your ad without our permission, YOU sued US."
GoldieBlox is one of four companies named as finalists in a competition held by software maker Intuit to pay millions for a Super Bowl advertisement for the winner. The company's Girls video is not part of the competition.
- AP