Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is a human coronavirus (HCoV) that has created a pandemic situation worldwide as COVID-19. This virus can invade human cells via angiotensin-converting enzyme 2 (ACE2) receptor-based mechanisms, affecting the human respiratory tract. However, several reports of neurological symptoms suggest a neuroinvasive development of coronavirus. SARS-CoV-2 can damage the brain via several routes, along with direct neural cell infection with the coronavirus. The chronic inflammatory reactions surge the brain with proinflammatory elements, damaging the neural cells, causing brain ischemia associated with other health issues. SARS-CoV-2 exhibited neuropsychiatric and neurological manifestations, including cognitive impairment, depression, dizziness, delirium, and disturbed sleep. These symptoms show nervous tissue damage that enhances the occurrence of neurodegenerative disorders and aids dementia. SARS-CoV-2 has been seen in brain necropsy and isolated from the cerebrospinal fluid of COVID-19 patients. The associated inflammatory reaction in some COVID-19 patients has increased proinflammatory cytokines, which have been investigated as a prognostic factor. Therefore, the immunogenic changes observed in Parkinson’s and Alzheimer’s patients include their pathogenetic role. Inflammatory events have been an important pathophysiological feature of neurodegenerative diseases (NDs) such as Parkinson’s and Alzheimer’s. The neuroinflammation observed in AD has exacerbated the Aβ burden and tau hyperphosphorylation. The resident microglia and other immune cells are responsible for the enhanced burden of Aβ and subsequently mediate tau phosphorylation and ultimately disease progression. Similarly, neuroinflammation also plays a key role in the progression of PD. Several studies have demonstrated an interplay between neuroinflammation and pathogenic mechanisms of PD. The dynamic proinflammation stage guides the accumulation of α-synuclein and neurodegenerative progression. Besides, few viruses may have a role as stimulators and generate a cross-autoimmune response for α-synuclein. Hence, neurological complications in patients suffering from COVID-19 cannot be ruled out. In this review article, our primary focus is on discussing the neuroinvasive effect of the SARS-CoV-2 virus, its impact on the blood-brain barrier, and ultimately its impact on the people affected with neurodegenerative disorders such as Parkinson’s and Alzheimer’s.