The episode, titled “Loan-A Lisa”, is set to be shown in the autumn, around the same time that a biopic of the 26-year-old’s life is released.
Scripted by Aaron Sorkin, The Social Network is based on a controversial book about Facebook which alleges that Mr Zuckerberg stole the idea for the site.
Facebook was created in 2004 and now has 500 million users. According to Forbes Magazine Mr Zuckerberg is the youngest billionaire in the world.
Watch the trailer for The Social Network here