Born and raised in Karachi, Hoodbhoy studied at the Massachusetts Institute of Technology for nine years, where he received degrees in electrical engineering, mathematics and solid-state physics, eventually leading to a PhD in nuclear physics. In 1981, Hoodbhoy went on to conduct post-doctoral research at the University of Washington, before leaving to serve as a visiting professor at the Carnegie Mellon University in 1985. While still a professor at the Quaid-e-Azam University, Hoodbhoy worked as a guest scientist at the International Centre for Theoretical Physics from 1986 to 1994. He remained with the Quaid-e-Azam University until 2010, throughout which he held visiting professorships at MIT, University of Maryland and Stanford Linear Collider.