Background: Nanosilver possesses antiviral, antibacterial, anti-inflammatory, anti-angiogenesis, antiplatelet, and anticancer properties. The development of disinfectants, inactivated vaccines, and combined etiotropic and immunomodulation therapy against respiratory viral infections, including COVID-19, remains urgent. Aim: Our goal was to determine the SARS-CoV-2 molecular targets (genomic RNA and the structural virion proteins S and N) for silver-containing nanomaterials. Methods: SARS-CoV-2 gene cloning, purification of S2 and N recombinant proteins, viral RNA isolation from patients’ blood samples, reverse transcription with quantitative real-time PCR ((RT)2-PCR), ELISA, and multiplex immunofluorescent analysis with magnetic beads (xMAP) for detection of 17 inflammation markers. Results: Fluorescent Ag nanoclusters (NCs) less than 2 nm with a few recovered silver atoms, citrate coated Ag nanoparticles (NPs) with diameters of 20–120 nm, and nanoconjugates of 50–150 nm consisting of Ag NPs with different protein envelopes were constructed from AgNO3 and analyzed by means of transmission electron microscopy (TEM), atomic force microscopy (AFM), ultraviolet-visible light absorption, and fluorescent spectroscopy. SARS-CoV-2 RNA isolated from COVID-19 patients’ blood samples was completely cleaved with the artificial RNase complex compound Li+[Ag+2Cys2−(OH−)2(NH3)2] (Ag-2S), whereas other Ag-containing materials provided partial RNA degradation only. Treatment of the SARS-CoV-2 S2 and N recombinant antigens with AgNO3 and Ag NPs inhibited their binding with specific polyclonal antibodies, as shown by ELISA. Fluorescent Ag NCs with albumin or immunoglobulins, Ag-2S complex, and nanoconjugates of Ag NPs with protein shells had no effect on the interaction between coronavirus recombinant antigens and antibodies. Reduced production of a majority of the 17 inflammation biomarkers after treatment of three human cell lines with nanosilver was demonstrated by xMAP. Conclusion: The antiviral properties of the silver nanomaterials against SARS-CoV-2 coronavirus differed. The small-molecular-weight artificial RNase Ag-2S provided exhaustive RNA destruction but could not bind with the SARS-CoV-2 recombinant antigens. On the contrary, Ag+ ions and Ag NPs interacted with the SARS-CoV-2 recombinant antigens N and S but were less efficient at performing viral RNA cleavage. One should note that SARS-CoV-2 RNA was more stable than MS2 phage RNA. The isolated RNA of both the MS2 phage and SARS-CoV-2 were more degradable than the MS2 phage and coronavirus particles in patients’ blood, due to the protection with structural proteins. To reduce the risk of the virus resistance, a combined treatment with Ag-2S and Ag NPs could be used. To prevent cytokine storm during the early stages of respiratory infections with RNA-containing viruses, nanoconjugates of Ag NPs with surface proteins could be recommended.