The phenoxazine scaffold is widely used to stabilize nucleic acid duplexes, as a part of fluorescent probes for the study of nucleic acid structure, recognition, and metabolism, etc. Here we present the synthesis of phenoxazine-based nucleoside derivatives and their antiviral activity against a panel of structurally diverse viruses: enveloped DNA herpesviruses varicella zoster virus (VZV) and human cytomegalovirus, enveloped RNA tick-borne encephalitis virus (TBEV), and non-enveloped RNA enteroviruses. Studied compounds were effective against DNA and RNA viruses reproduction in cell culture. 3-(2′-Deoxy-β-D-ribofuranosyl)-1,3-diaza-2-oxophenoxazine proved to be a potent inhibitor of VZV replication with superior activity against wild type than thymidine kinase deficient strains (EC 50 0.06 and 10 μM, respectively). This compound did not show cytotoxicity on all the studied cell lines. Several compounds showed promising activity against TBEV (EC 50 0.35–0.91 μM), but the activity was accompanied by pronounced cytotoxicity. These compounds may be considered as a good starting point for further structure optimization as antiherpesviral or antiflaviviral compounds.