SARS-CoV-2 can infect multiple organs, including lung, intestine, kidney, heart, liver, and brain. The molecular details of how the virus navigates through diverse cellular environments and establishes replication are poorly defined. Here, we performed global proteomic analysis of the virus-host interface in a newly established panel of phenotypically diverse, SARS-CoV-2-infectable human cell lines representing different body organs. This revealed universal inhibition of interferon signaling across cell types following SARS-CoV-2 infection. We performed systematic analyses of the JAK-STAT pathway in a broad range of cellular systems, including immortalized cell lines and primary-like cardiomyocytes, and found that several pathway components were targeted by SARS-CoV-2 leading to cellular desensitization to interferon. These findings indicate that the suppression of interferon signaling is a mechanism widely used by SARS-CoV-2 in diverse tissues to evade antiviral innate immunity, and that targeting the viral mediators of immune evasion may help block virus replication in patients with COVID-19.