The self-assembly of the Nucleocapsid protein (NCAP) of SARS-CoV-2 is crucial for its function. Computational analysis of the amino acid sequence of NCAP reveals low-complexity domains (LCDs) akin to LCDs in other proteins known to self-assemble as phase separation droplets and amyloid fibrils. Previous reports have described NCAP's propensity to phase-separate. Here we show that the central LCD of NCAP is capable of both, phase separation and amyloid formation. Within this central LCD we identified three adhesive segments and determined the atomic structure of the fibrils formed by each. Those structures guided the design of G12, a peptide that interferes with the self-assembly of NCAP and demonstrates antiviral activity in SARS-CoV-2 infected cells. Our work, therefore, demonstrates the amyloid form of the central LCD of NCAP and suggests that amyloidogenic segments of NCAP could be targeted for drug development.