Although animal models have been evaluated for severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection, none have fully recapitulated the lung disease phenotypes seen in humans who have been hospitalized. Here, we evaluate transgenic mice expressing the human angiotensin I-converting enzyme 2 (ACE2) receptor driven by the cytokeratin-18 (K18) gene promoter (K18-hACE2) as a model of SARS-CoV-2 infection. Intranasal inoculation of SARS-CoV-2 in K18-hACE2 mice results in high levels of viral infection in lungs, with spread to other organs. A decline in pulmonary function occurs 4 days after peak viral titer and correlates with infiltration of monocytes, neutrophils and activated T cells. SARS-CoV-2-infected lung tissues show a massively upregulated innate immune response with signatures of nuclear factor-κB-dependent, type I and II interferon signaling, and leukocyte activation pathways. Thus, the K18-hACE2 model of SARS-CoV-2 infection shares many features of severe COVID-19 infection and can be used to define the basis of lung disease and test immune and antiviral-based countermeasures.