A range of psychiatric disorders has been recognized with coronavirus disease 2019 (COVID-19) infection, including acute stress, anxiety, depression, suicidal behavior, and post-traumatic stress disorder. Among those, the most worrying is death by suicide, which has been associated with COVID-19-related psychiatric disorders and psychosocial stressors. We report the first two cases of death by suicide, unlikely due to any current psychiatric disorders, while undergoing treatment in two inpatient facilities designated for COVID-19 patients. Case 1 was a 40-year-old man who presented to the emergency department with symptoms of a viral infection. This led to the diagnosis of COVID-19. While undergoing treatment in an inpatient facility, 3 weeks later, he died by hanging. Case 2 was a 25-year-old man with COVID-19-related upper respiratory tract symptoms and a possible undiagnosed pre-existing anxiety disorder. While undergoing treatment in a medical unit of a COVID-19-designated hospital, a week after the diagnosis of COVID-19, the patient died after jumping off the multistory hospital building. In both cases, there had been a diagnosis of COVID-19, and treatment was provided within an inpatient facility. Both patients were unvaccinated and had no evidence of a current psychiatric disorder or any warning signs of suicidal intent. Death by suicide can occur in COVID-19 patients without any warning signs of a psychiatric disorder or evidence of any apparent distress. Therefore, even without a diagnosable mental disorder, clinicians should still be vigilant about potential suicidal risk in patients with COVID-19 infection.