Some viruses restructure host chromatin, influencing gene expression, with implications for disease outcome. Whether this occurs for SARS-CoV-2, the virus causing COVID-19, is largely unknown. Here we characterized the 3D genome and epigenome of human cells after SARS-CoV-2 infection, finding widespread host chromatin restructuring that features widespread compartment A weakening, A-B mixing, reduced intra-TAD contacts and decreased H3K27ac euchromatin modification levels. Such changes were not found following common-cold-virus HCoV-OC43 infection. Intriguingly, the cohesin complex was notably depleted from intra-TAD regions, indicating that SARS-CoV-2 disrupts cohesin loop extrusion. These altered 3D genome/epigenome structures correlated with transcriptional suppression of interferon response genes by the virus, while increased H3K4me3 was found in the promoters of pro-inflammatory genes highly induced during severe COVID-19. These findings show that SARS-CoV-2 acutely rewires host chromatin, facilitating future studies of the long-term epigenomic impacts of its infection.