Panag started her education in Sangrur, in Punjab. Her father was in the army and the family moved to different places across India and abroad. As a result of this, she studied in 14 different schools including Kendriya Vidyalayas (Chandigarh, Mhow, Leh and Wellington, Tamil Nadu), The Lawrence School, Lovedale and the International School of Lusaka, Zambia. She did her Bachelors in Mathematics from Punjabi University, Patiala, and Masters in Political Science from Panjab University, Chandigarh. As a student, Panag was interested in sports and public speaking. She won numerous state and national level debate competitions, including two gold medals at the Annual National Inter University Debate competition.