Hemagglutinin (HA), the class I influenza A virus protein is responsible for the attachment of virus particles to the cell by binding to glycan receptors, subsequent virion internalization, and cell entry. Consequently, the importance of HA makes it a primary target for the development of anti-influenza drugs. The natural oligoribonucleotides (ORNs) as well as their derivatives functionalized with D-mannitol (ORNs-D-M) possess anti-influenza properties in vitro and in vivo due to interaction with HA receptor sites. This activity suppresses the viral infection in host cells. In the present work, the complexes of ORNs and ORNs-D-M with HA protein were studied by agglutination assay, fluorescence spectroscopy, as well as molecular docking simulations. Acquired experimental data exhibited a decrease in HA titer by 32 times after incubation with the ORNs-D-M for 0.5–24 h. Quenching fluorescence intensity of the HA suggests that titration by ORNs and ORNs-D-M probably leads to changes in the HA structure. Detailed structural data were obtained with the molecular docking simulations performed for ORNs and ORNs-D-M ligands containing three and six oligoribonucleotides. The results reveal that a majority of the ORNs and ORNs-D-M bind in a non-specific way to the receptor-binding domain of the HA protein. The ligand’s affinity to the hemagglutinin was estimated at the micromolar level. Presented experimental data confirmed that both natural ORNs and functionalized ORNs-D-M inhibit the interactions between HA and glycan receptors and demonstrate anti-influenza activity.