Broad-spectrum antiviral agents that are effective against many viruses are difficult to develop, as the key molecules, as well as the biochemical pathways by which they cause infection, differ largely from one virus to another. This was more strongly highlighted by the COVID-19 pandemic, which found health systems all over the world largely unprepared and proved that the existing armamentarium of antiviral agents is not sufficient to address viral threats with pandemic potential. The clinical protocols for the treatment of COVID-19 are currently based on the use of inhibitors of the inflammatory cascade (dexamethasone, baricitinib), or inhibitors of the cytopathic effect of the virus (monoclonal antibodies, molnupiravir or nirmatrelvir/ritonavir), using different agents. There is a critical need for an expanded armamentarium of orally bioavailable small-molecular medicinal agents, including those that possess dual antiviral and anti-inflammatory (AAI) activity that would be readily available for the early treatment of mild to moderate COVID-19 in high-risk patients. A multidisciplinary approach that involves the use of in silico screening tools to identify potential drug targets of an emerging pathogen, as well as in vitro and in vivo models for the determination of a candidate drug’s efficacy and safety, are necessary for the rapid and successful development of antiviral agents with potentially dual AAI activity. Characterization of candidate AAI molecules with physiologically based pharmacokinetics (PBPK) modeling would provide critical data for the accurate dosing of new therapeutic agents against COVID-19. This review analyzes the dual mechanisms of AAI agents with potential anti-SARS-CoV-2 activity and discusses the principles of PBPK modeling as a conceptual guide to develop new pharmacological modalities for the treatment of COVID-19.