The coronavirus disease 2019 (COVID-19) vaccine was launched in India on 16 January 2021, prioritising health care workers which included medical students. We aimed to assess vaccine hesitancy and factors related to it among medical students in India. An online questionnaire was filled by 1068 medical students across 22 states and union territories of India from 2 February to 7 March 2021. Vaccine hesitancy was found among 10.6%. Concern regarding vaccine safety and efficacy, lack of awareness regarding their eligibility for vaccination and lack of trust in government agencies predicted COVID-19 vaccine hesitancy among medical students. On the other hand, the presence of risk perception regarding themselves being affected with COVID-19 reduced vaccine hesitancy as well as hesitancy in participating in COVID-19 vaccine trials. Vaccine-hesitant students were more likely to derive information from social media and less likely from teachers at their medical colleges. Choosing between the two available vaccines (Covishield and Covaxin) was considered important by medical students both for themselves and for their future patients. Covishield was preferred to Covaxin by students. Majority of those willing to take the COVID-19 vaccine felt that it was important for them to resume their clinical posting, face-to-face classes and get their personal life back on track. Around three-fourths medical students viewed that COVID-19 vaccine should be made mandatory for both health care workers and international travellers. Prior adult vaccination did not have an effect on COVID-19 vaccine hesitancy. Targeted awareness campaigns, regulatory oversight of vaccine trials and public release of safety and efficacy data and trust building activities could further reduce COVID-19 vaccine hesitancy among medical students.