Background Burn and trauma injuries need emergency care and resuscitation, which required uninterrupted delivery of inpatient care services during the coronavirus disease 2019 (COVID-19) pandemic. Burn patients are physiologically immunocompromised, increasing the risk of COVID-19 infection in them. This study analyzes the impact of COVID-19 pandemic on patient trends in a burn and plastic unit and assesses the effect of COVID-19 infection in burns. Methods This single-center, retrospective observational case–control study was conducted in the Department of Burns, Plastic and Maxillofacial Surgery of a tertiary care hospital in New Delhi, India. Patient data was collected from April 1, 2019 to August 10, 2019 and from April 1, 2020 to August 10, 2020. All data of burns and trauma patients collected was analyzed and compared. Results There were total 350 admissions during COVID time period and 562 admissions during non-COVID time period. The admission rate, type of burn injury, and death rate did not vary significantly during the two time periods. Thermal burn was the most common type of burn injury. There were total 18 cases diagnosed to be COVID-19 positive during the pandemic. There were two deaths among COVID-19 positive burn cases. Conclusion This study finds no difference in patient patterns during COVID and non-COVID time period. Amongst burn patients, no increased risk of COVID-19 infection is seen with larger body surface area of burns. No increase in mortality is seen in burn patients infected with COVID-19.