The molecular interactions between the amyloid fibrils from Aβ-peptide, insulin and α-synuclein and fullerenes of different sizes, including C20, C36, C60, C70, and C84, have been studied using the molecular docking approach. The fullerenes are found to bind to the loop or turn region of Aβ- and α-synuclein fibrillar assemblies, but reside at the end of insulin amyloid fibers, reflecting the lower affinity of carbon nanostructures to the latter aggregated protein. For all systems studied here, the fullerene binding to amyloid fibrils is size-dependent, with larger fullerenes exhibiting a higher binding affinity and a lower total energy of complexation. The analysis of side chain contacts highlights the pivotal role of van der Waals forces, specifically, alkyl and π-alkyl interactions, in the stabilization of the fullerene-amyloid complexes. The results obtained are discussed in terms of novel nanocomposite materials based on carbon nanoparticles and fibrillar proteins, as well as of the fullerene role in anti-amyloid therapy.