Nucleic-acid-based drugs are a promising class of novel therapeutics; however, their use in medicine is widely limited because of insufficient delivery into cells. This article proposes a new delivery strategy of nucleic acid fragments into cells as components of TiO2-based nanocomposites. For the first time, unmodified Dz molecules were non-covalently immobilized on TiO2 nanoparticles precovered with polylysine (TiO2•PL) with the formation of (TiO2•PL)•Dz nanocomposites. DNAzymes in the proposed nanocomposites were shown to retain their ability to cleave the RNA target in a cell-free system with the same selectivity as unbound Dz molecules. It was shown by confocal laser microscopy that the fluorescein-labelled (TiO2•PL)•DzFlu nanocomposites penetrate into eukaryotic cells, where DzFlu is internalized in the cytoplasm and predominantly in nuclei. Delivery of deoxyribozymes into cells in the proposed nanocomposites permits very efficient interactions with RNA targets inside cells. This was demonstrated by an example of inhibition of H5N1 influenza A virus replication (inhibition by a factor of ca. 3000). This effect was one order of magnitude higher than with using lipofectamine as the transfection agent. The proposed (TiO2•PL)•Dz nanocomposites demonstrated high antiviral activity and are thus potent as nucleic-acid-based drugs.