Self-assembling nanoparticles (saNP) and nanofibers were found in the recombinant coronavirus SARS-CoV-2 S1, S2, RBD and N proteins purified by affinity chromatography using Ni Sepharose. Scanning electron (SEM), atomic force (AFM) microscopy on mica or graphite surface and in liquid as well as dynamic light scattering (DLS) revealed nanostructures of various sizes. AFM in liquid cell without drying on the surface showed mean height of S1 saNP 80.03 nm, polydispersity index (PDI) 0.006; for S2 saNP mean height 93.32 nm, PDI = 0.008; for N saNP mean height 16.71 nm, PDI = 0.99; for RBD saNP mean height 16.25 nm, PDI = 0.55. Ratios between the height and radius of each saNP in the range 0.1-0.5 suggested solid protein NP but not vesicles with internal empty spaces. The solid but not empty structures of the protein saNP were also confirmed by STEM after treatment of saNP with the standard contrasting agent uranyl acetate. The saNP remained stable after multiple freeze-thaw cycles in water and hyperosmotic solutions for 2 years at -20 °C. Receptor-mediated penetration of the SARS-CoV-2 S1 and RBD saNP in the African green mokey kidney Vero cells with the specific receptors for β-coronavirus reproduction was more efficient compared to unspecific endocytosis into MDCK cells without the specific receptors. Amyloid-like structures were revealed in the SARS-CoV-2 S1, S2, RBD and N saNP by means of their interaction with Thioflavin T and Congo Red dyes. Taken together, spontaneous formation of the amyloid-like self-assembling nanostructures due to the internal affinity of the SARS-CoV-2 virion proteins might induce proteinopathy in patients, including conformational neurodegenerative diseases, change stability of vaccines and diagnostic systems.