Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2), responsible for COVID-19 pandemic, caused catastrophic health and social effects, but little is known about its consequences on mental health. Other viral infections have been associated with psychiatric sequelae: infection-triggered disturbing of the immune system and the stressful intensive unit care can cause psychological and psychiatric complications. Moreover, SARS-CoV-2 can potentially induce neuronal injuries, leading to neurocognitive disabilities. Previous studies during the COVID-19 pandemic reported a high occurrence rate of psychopathological and neurocognitive conditions among COVID-19 survivors, highlighting the need for screening for these impairments in order to implement early interventions and secondary prevention. However, many psychiatric disorders can take several years to develop, and it is still difficult to differentiate between factors linked to the infection itself or to the global context of the pandemic. In this review, we describe the effects of SARS-CoV-2 infection on mental health, the mechanisms involved in psychiatric and neurocognitive sequelae, and the strategies of prevention and management. More studies are needed to investigate the effects of a range of factors including clinical, sociodemographic, and inflammatory predictors. These efforts could be useful to identify high-risk individuals and inform targeted preventive actions.