As an actor, he is known for his role portraying Dr. Lawrence Kutner on the television program House, as well as the character Kumar Patel in the Harold and Kumar film series. He is also recognized for his performance in the critically acclaimed film, The Namesake. Additionally, Penn has taught at the University of Pennsylvania in the Cinema Studies Program as a visiting lecturer.

On April 8, 2009, it was announced that Penn would join the Obama administration as an Associate Director in the White House Office of Public Engagement. This necessitated that his character, Lawrence Kutner, be written out of the TV series House.