The antiviral drug Molnupiravir (MOL) and its conjugate with Hyaluronic Acid (HA-MOL) demonstrate the significance of targeting the main protease (Mpro) and papain-like protease (PLpro) of SARS-CoV-2. The pure drug Molnupiravir and the designed polymer-drug conjugate using Molnupiravir and hyaluronic acid were evaluated through molecular docking, pharmacokinetic analysis, molecular dynamics studies, and Density Functional Theory (DFT) studies, focusing on their ability to inhibit Mpro and PLpro proteins, which are essential for SARS-CoV-2 replication and transmission. Results indicate that the HA-MOL conjugate exhibits superior activity against these target proteins compared to the pure drug. ADMET analysis further showed that the HA conjugate has enhanced pharmacokinetic properties over the free form of the drug. Molecular dynamics simulation studies of Molnupiravir and HA-MOL revealed robust MD simulation trajectories with the SARS-CoV-2 target proteins. DFT analysis indicates that the polymer-conjugated drug significantly enhances electrophilicity in the gas phase and stabilizes the drug in aqueous environments, supporting its effectiveness in biological systems for drug delivery. This study concludes that the Hyaluronic Acid-Molnupiravir conjugate is a promising new therapeutic that may offer enhanced control over the SARS-CoV-2 virus.