Born in Lahore, Siddiqa studied at Kinnaird College and went on to join the Civil Service of Pakistan. As a civil servant, Siddiqa served as the director of naval research with the Pakistan Navy, making her the first civilian and the first woman to work at that position in Pakistan's defence establishment. She also worked in military accounts and as deputy director Defense Services Audit. Siddiqa moved to London, where she received her PhD from King's College London in war studies. After leaving the civil service, she served as the senior research fellow at the Sandia National Laboratories and went on to teach at the University of Pennsylvania, Johns Hopkins University and the Quaid-e-Azam University. She also served as the Charles Wallace Fellow at St Antony's College, Oxford in 2015.