The COVID-19 pandemic has strongly impacted daily life across the globe and caused millions of infections and deaths. No drug therapy has yet been approved for the clinic. In the current study, we provide a novel nanoformulation against DNA and RNA viruses that also has a potential for implementation against COVID-19. The inorganic–organic hybrid nanoformulation is composed of zinc oxide nanoparticles (ZnO NPs) functionalized with triptycene organic molecules (TRP) via EDC/NHS coupling chemistry and impregnated with a natural agent, ellagic acid (ELG), via non-covalent interactions. The physicochemical properties of prepared materials were identified with several techniques. The hybrid nanoformulation contained 9.5 wt.% TRP and was loaded with up to 33.3 wt.% ELG. ELG alone exhibited higher cytotoxicity than both the ZnO NPs and nanoformulation against host cells. The nanoformulation efficiently inhibited viruses, compared to ZnO NPs or ELG alone. For H1N1 and HCoV-229E (RNA viruses), the nanoformulation had a therapeutic index of 77.3 and 75.7, respectively. For HSV-2 and Ad-7 (DNA viruses), the nanoformulation had a therapeutic index of 57.5 and 51.7, respectively. In addition, the nanoformulation showed direct inactivation of HCoV-229E via a virucidal mechanism. The inhibition by this mechanism was > 60%. Thus, the nanoformulation is a potentially safe and low-cost hybrid agent that can be explored as a new alternative therapeutic strategy for COVID-19.