The severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) causing the COVID-19 respiratory disease pandemic utilizes unique 2'-O-methyltransferase (2'-O-MTase) capping machinery to camouflage its RNA from innate immune recognition. The nsp16 catalytic subunit of the 2'-O-MTase is unusual in its requirement for a stimulatory subunit (nsp10) to catalyze the ribose 2'-O-methylation of the viral RNA cap. Here we provide a computational basis for drug repositioning or de novo drug development based on three differential traits of the intermolecular interactions of the SARS-CoV-2-specific nsp16/nsp10 heterodimer, namely: (1) the S-adenosyl-l-methionine-binding pocket of nsp16, (2) the unique "activating surface" between nsp16 and nsp10, and (3) the RNA-binding groove of nsp16. We employed ≈9000 U.S. Food and Drug Administration (FDA)-approved investigational and experimental drugs from the DrugBank repository for docking virtual screening. After molecular dynamics calculations of the stability of the binding modes of high-scoring nsp16/nsp10-drug complexes, we considered their pharmacological overlapping with functional modules of the virus-host interactome that is relevant to the viral lifecycle, and to the clinical features of COVID-19. Some of the predicted drugs (e.g., tegobuvir, sonidegib, siramesine, antrafenine, bemcentinib, itacitinib, or phthalocyanine) might be suitable for repurposing to pharmacologically reactivate innate immune restriction and antagonism of SARS-CoV-2 RNAs lacking 2'-O-methylation.