The coronavirus pandemic is an unending global epidemic of coronavirus disease 2019 (commonly known as, COVID-19) caused by SARS-CoV-2 (Severe Acute Respiratory Syndrome CoronaVirus 2) that was first reported in Wuhan city of China at the end of the year 2019. Unfortunately, there was no oral antiviral drug for the treatment of this pandemic, which was urgently needed. Recently, after the phase 3 trial, researchers have reported the tolerability, safety profile and antiviral efficacy of Molnupiravir in the treatment of COVID-19. Topological indices are used to determine different physico-chemical, pharmaceutical and biological attributes of a molecular graph. In the current study, we depict the two-dimensional graph structure of the hydrogen-suppressed Molnupiravir. We calculate the values of some well-known degree-based topological indices for Molnupiravir drug by their standard definitions and alternatively by using M-polynomial approach which is more compact and appropriate. Among these indices, we obtain that the augmented Zagreb and modified second Zagreb indices have maximum and minimum values, respectively. Additionally, we geometrically represent the topological indices in increasing order and surface nature of the M-polynomial. The results obtained can help the researchers to study the pharmacokinetic properties of the newly developed drugs used in the treatment of COVID-19.