The COVID-2019 pandemic is the most severe acute public health threat of the twenty-first century. To properly address this crisis with both robust testing and novel treatments, we require a deep understanding of the life cycle of the causative agent, the SARS-CoV-2 coronavirus. Here, we examine the architecture and self-assembly properties of the SARS-CoV-2 nucleocapsid (N) protein, which binds viral RNA and assembles into a filament that is packaged into new virions. We determined a 1.4 Å resolution crystal structure of this protein's N2b domain, revealing a compact, intertwined dimer very similar to that of related coronaviruses SARS-CoV and MERS-CoV. Using size exclusion chromatography and multi-angle light scattering, we find that this domain forms a dimer in solution, and that addition of the C-terminal spacer B/N3 domain mediates tetramer formation. Using hydrogen-deuterium exchange mass spectrometry, we find evidence that at least part of this putatively disordered domain is structured, potentially forming an α-helix that either self-associates or docks against the N2b domain to mediate tetramer formation. Finally, we map the locations of over 4,400 individual amino acid substitutions in the N protein from ~17,000 SARS-CoV-2 genome sequences, and find that they are strongly clustered in the protein's N2a linker domain. The nearly 300 substitutions identified within the N1b and N2b domains cluster away from their functional RNA binding and dimerization interfaces. Overall, this work reveals the architecture and self-assembly properties of a key protein in the SARS-CoV-2 life cycle. As the N protein is a common target of patient antibodies, this work will also benefit ongoing efforts to develop robust and specific serological tests, and could also benefit the analysis of patient-derived antibodies.