Akhtar was born in Staten Island, New York City, to Pakistani parents. After spending most of his childhood in Milwaukee, Wisconsin, he attended Brown University where he majored in theater. After graduation he moved to Italy and studied acting with Jerzy Grotowski for a year. He then returned to the US to teach acting classes with Andre Gregory and earn his M.A. in directing from Columbia University School of the Arts. While at Columbia he and classmates Tom Glynn and Joseph Castelo formed the idea for The War Within, a film about an ordinary man radicalized into becoming a terrorist. Akhtar also starred in the film playing Hassan, the would-be terrorist. In 2011 he played Neel Kashkari in the HBO film Too Big to Fail.
Akhtar has written for the stage. His playwriting credits include Disgraced, which premiered at The American Theater Company in January 2012 and which was staged at Lincoln Center in New York in October 2012, and won the 2013 Pulitzer Prize for Drama. The play's New York cast included actors Aasif Mandvi, Heidi Armbruster, Erik Jensen and Karen Pittman.