Enveloped viruses infect cells via fusion between the viral envelope and a cellular membrane. This membrane fusion process is driven by viral proteins, but slow stochastic protein activation dominates the fusion kinetics, making it challenging to probe the role of membrane mechanics in viral entry directly. Furthermore, many changes to the interacting membranes alter the curvature, deformability, and spatial organization of membranes simultaneously. We have used bilayer-coated silica nanoparticles to restrict the deformability of lipid membranes in a controllable manner. The single-event kinetics for fusion of influenza virus to coated nanoparticles permits independent testing of how the membrane curvature and deformability control the free energy barriers to fusion. Varying the free energy of membrane deformation, but not membrane curvature, causes a corresponding response in the fusion kinetics and fusion protein stoichiometry. Thus, the main free energy barrier to lipid mixing by influenza virus is controlled by membrane deformability and not the initial membrane curvature.