The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection causes COVID-19, a pandemic that seriously threatens global health. SARS-CoV-2 propagates by packaging its RNA genome into membrane enclosures in host cells. The packaging of the viral genome into the nascent virion is mediated by the nucleocapsid (N) protein, but the underlying mechanism remains unclear. Here, we show that the N protein forms biomolecular condensates with viral genomic RNA both in vitro and in mammalian cells. Phase separation is driven, in part, by hydrophobic and electrostatic interactions. While the N protein forms spherical assemblies with unstructured RNA, it forms asymmetric condensates with viral RNA strands that contain secondary structure elements. Cross-linking mass spectrometry identified a region that forms interactions between N proteins in condensates, and truncation of this region disrupts phase separation. We also identified small molecules that alter the formation of N protein condensates. These results suggest that the N protein may utilize biomolecular condensation to package the SARS-CoV-2 RNA genome into a viral particle.