During co-evolution with their hosts, many viruses have evolved a membrane fusion mechanism to facilitate host cell entry. Examples are human immunodeficiency virus type 1 (HIV-1) and severe acute respiratory syndrome coronaviruses 1 and 2 (SARS-CoV-1 and SARS-CoV-2). These viruses can also infect immune cells (e.g., T cells), providing one of the possible mechanisms for the T cell lymphopenia observed in patients with these infections. Previously, we hypothesized and confirmed in vivo that like HIV-1, SARS-CoV-1 can use its fusion domain not only to enter the T cell but also to directly inhibit T cell receptor signaling. Here, based on the analysis of available structural and clinical data, we hypothesize that SARS-CoV-2 may use a similar "disarm the alarm" strategy to suppress immune responses. We also discuss the implications of this hypothesis for better understanding coronavirus disease 2019 (COVID-19) pathology, developing effective COVID-19 vaccines and improving clinical outcomes for COVID-19 patients.