As of today, influenza viruses remain a relevant target for the development of antiviral compounds due to their rapid evolution and acquisition of the resistance to existing drugs. Fullerene derivatives have already shown the ability to successfully interact with viruses, and polyhydrated fullerenes (or fullerenols) are particularly attractive due to their compatibility with biological fluids and low toxicity. Therefore, the goal of this work was to study the effect of two batches of a mixture of polyhydrated fullerenes with a mass ratio of 78.1% C60/C70and 21.9% C76/C78/C84on the influenza A (H1N1) virus. It was determined that the mixture of fullerenols, along with the low toxicity, showed high antiviral activity with a decrease in the viral infectious titer up to 4 orders of magnitude. In addition, studied fullerenols did not affect the hemagglutination process and did not show any significant prophylactic activity. With the help of molecular docking and molecular dynamics simulation, the likely target of fullerenols' action was determined—the binding site of the RNA primer of the viral RNA-dependent RNA polymerase. Therefore, we assume that the high antiviral effect of polyhydrated fullerenes on influenza A virus is related to their interaction with the viral RNA polymerase.