The main target for COVID-19 is the lung with the development of acute respiratory failure. But the virus also displays tropism to the central nervous, muscle, and immune systems. The paper gives the data available in the literature on nervous system damage and the characteristics of clinical and magnetic resonance imaging manifestations of brain damage in COVID-19. Among the neurological symptoms of COVID-19, there may be stroke, encephalitis, and neuropathy. An account is given of the features of multiple sclerosis patient management during the COVID-19 pandemic depending on the risk of developing coronavirus infection.