The event will take place in person next month, but with strict Covid safety measures in place for attendees.
Flag Day, which Penn also stars in alongside Josh Brolin, is an adaptation of the book by Jennifer Vogel.
It tells the story of a father who lives a double life as a counterfeiter, bank robber and conman in order to provide for his daughter.
Penn's previous directing efforts have included Into The Wild, The Pledge and The Crossing Guard.
Flag Day will also star Miles Teller and Eddie Marsan, alongside Penn's daughter Dylan.
It's one of several films organisers announced on Thursday for this year's festival, which will run from 6 to 17 July.