Long-term neurological and mental complications of COVID-19, the so-called post-COVID syndrome or long COVID, affect the quality of life. The most persistent manifestations of long COVID include fatigue, anosmia/hyposmia, insomnia, depression/anxiety, and memory/attention deficits. The physiological basis of neurological and psychiatric disorders is still poorly understood. This review summarizes the current knowledge of neurological sequelae in post-COVID patients and discusses brain demyelination as a possible mechanism of these complications with a focus on neuroimaging findings. Numerous reviews, experimental and theoretical studies consider brain demyelination as one of the mechanisms of the central neural system impairment. Several factors might cause demyelination, such as inflammation, direct effect of the virus on oligodendrocytes, and cerebrovascular disorders, inducing myelin damage. There is a contradiction between the solid fundamental basis underlying demyelination as the mechanism of the neurological injuries and relatively little published clinical evidence related to demyelination in COVID-19 patients. The reason for this probably lies in the fact that most clinical studies used conventional MRI techniques, which can detect only large, clearly visible demyelinating lesions. A very limited number of studies use specific methods for myelin quantification detected changes in the white matter tracts 3 and 10 months after the acute phase of COVID-19. Future research applying quantitative MRI assessment of myelin in combination with neurological and psychological studies will help in understanding the mechanisms of post-COVID complications associated with demyelination.