The coronavirus disease 2019 (COVID-19) pandemic has caused large-scale economic and social losses and worldwide deaths. Although most COVID-19 patients have initially complained of respiratory insufficiency, the presence of neuropsychiatric manifestations is also reported frequently, ranging from headache, hyposmia/anosmia, and neuromuscular dysfunction to stroke, seizure, encephalopathy, altered mental status, and psychiatric disorders, both in the acute phase and in the long term. These neuropsychiatric complications have emerged as a potential indicator of worsened clinical outcomes and poor prognosis, thus contributing to mortality in COVID-19 patients. Their etiology remains largely unclear and probably involves multiple neuroinvasive pathways. Here, we summarize recent animal and human studies for neurotrophic properties of severe acute respiratory syndrome coronavirus (SARS-CoV-2) and elucidate potential neuropathogenic mechanisms involved in the viral invasion of the central nervous system as a cause for brain damage and neurological impairments. We then discuss the potential therapeutic strategy for intervening and preventing neuropsychiatric complications associated with SARS-CoV-2 infection. Time-series monitoring of clinical–neurochemical–radiological progress of neuropsychiatric and neuroimmune complications need implementation in individuals exposed to SARS-CoV-2. The development of a screening, intervention, and therapeutic framework to prevent and reduce neuropsychiatric sequela is urgently needed and crucial for the short- and long-term recovery of COVID-19 patients.