In the present study, a highly effective carrier system has been developed for the delivery of antiviral siRNA mixtures. The developed hybrid microcarriers, made of biodegradable polymers and SiO2 nanostructures, more efficiently mediate cellular uptake of siRNA than commercially available liposome-based reagents and polyethyleneimine (PEI); they also demonstrate low in vitro toxicity and protection of siRNA from RNase degradation. A series of siRNA designs (targeting the most conserved regions of three influenza A virus (IAV) genes: NP, NS, and PA) were screened in vitro using RT-qPCR, ELISA analysis, and hemagglutination assay. Based on the results of screening, the three most effective siRNAs (PA-1630, NP-717, and NS-777) were selected for in situ encapsulation into hybrid microcarriers. It was revealed that pre-treatment of cells with a mixture of PA-1630, NP-717, and NS-777 siRNAs, delivered by hybrid microcarriers, provided stronger inhibition of viral M1 mRNA expression and control of NP protein level, after viral infection, than single pre-treatment by any of three encapsulated siRNAs used in the study. Moreover, the effective inhibition of replication in several IAV subtypes (H1N1, H1N1pdm, H5N2, and H7N9) using a cocktail of the three selected siRNAs, delivered by our hybrid capsules to the cells, was achieved. In conclusion, we have developed a proof-of-principle which shows that our hybrid microcarrier technology (utilizing a therapeutic siRNA cocktail) may represent a promising approach in anti-influenza therapy.