Novel coronavirus SARS-CoV-2 and COVID-19, besides affecting the respiratory system, may lead to central and peripheral nervous system disorders and also cause muscular symptoms. The authors review the literature and own clinical case with respect to nervous system involvement in COVID-19 patients. There is a correlation between the severity of COVID-19 and the severity and frequency of neurologic complications. Severe neurologic symptoms are primarily observed in patients with severe COVID-19. Neurologic-associated symptoms may include stroke, acute necrotizing encephalopathy, and Guillen—Barre syndrome. Diseases that potentially aggravate COVID-19 and increase the risk of neurologic complications include arterial hypertension, diabetes, chronic diseases of the heart and respiratory system. The probable impact of human coronaviruses on chronic and progressive diseases of the nervous system with particular respect to multiple sclerosis is reviewed. A triage plan for stroke and MS patients during the COVID-19 pandemic, depending on the risk of coronavirus infection, is presented.