Diabetes mellitus (DM) is one of the most common comorbid conditions in persons with COVID-19 and a risk factor for poor prognosis. The reasons why COVID-19 is more severe in persons with DM are currently unknown although the scarce data available on patients with DM hospitalized because of COVID-19 show that glycemic control is inadequate. The fact that patients with COVID-19 are usually cared for by health professionals with limited experience in the management of diabetes and the need to prevent exposure to the virus may also be obstacles to glycemic control in patients with COVID-19. Effective clinical care should consider various aspects, including screening for the disease in at-risk persons, education, and monitoring of control and complications. We examine the effect of COVID-19 on DM in terms of glycemic control and the restrictions arising from the pandemic and assess management of diabetes and drug therapy in various scenarios, taking into account factors such as physical exercise, diet, blood glucose monitoring, and pharmacological treatment. Specific attention is given to patients who have been admitted to hospital and critically ill patients. Finally, we consider the role of telemedicine in the management of DM patients with COVID-19 during the pandemic and in the future.