A deeper understanding of the molecular biology of SARS-CoV-2 infection, including the host response to the virus, is urgently needed. Commonalities exist between the host immune response to viral infections and cancer. Here, we defined transcriptional signatures of SARS-CoV-2 infection involving hundreds of genes common across lung adenocarcinoma cell lines (A549, Calu-3) and normal human bronchial epithelial cells (NHBE), with additional signatures being specific to one or both adenocarcinoma lines. Cross-examining eight transcriptomic databases, we found that host transcriptional responses of lung adenocarcinoma cells to SARS-CoV-2 infection shared broad similarities with host responses to multiple viruses across different model systems and patient samples. Furthermore, these SARS-CoV-2 transcriptional signatures were manifested within specific subsets of human cancer, involving ~ 20% of cases across a wide range of histopathological types. These cancer subsets show immune cell infiltration and inflammation and involve pathways linked to the SARS-CoV-2 response, such as immune checkpoint, IL-6, type II interferon signaling, and NF-κB. The cell line data represented immune responses activated specifically within the cancer cells of the tumor. Common genes and pathways implicated as part of the viral host response point to therapeutic strategies that may apply to both SARS-CoV-2 and cancer.