The SARS-CoV-2 virus is responsible of COVID-19 affecting millions of humans around the world. COVID-19 shows diverse clinical symptoms (fever, cough, fatigue, diarrhea, body aches, headaches, anosmia and hyposmia). Approximately 30% of the patients with COVID-19 showed neurological symptoms, these going from mild to severe manifestations including headache, dizziness, impaired consciousness, encephalopathy, anosmia, hypogeusia, hyposmia, psychology and psychiatry among others. The neurotropism of SARS-CoV-2 virus explains its neuroinvasion provoking neurological damage as acute demyelination, neuroinflammation etc. At molecular level, the COVID-19 patients had higher levels of cytokines and chemokines known as cytokines storms which disrupt the blood brain barrier allowing the entrance of monocytes and lymphocytes causing neuroinflammation, neurodegeneration and demyelination. In addition, ischemic, hemorrhagic strokes, seizures and encephalopathy have been observed due to the proinflammatory cytokines. In this sense, to avoid or decrease neurological damage due to SARS-CoV-2 infection, an early neuroprotective management should be adopted. Several approaches can be used; one of them includes the use of HDAC inhibitors (HDACi) due to their neuroprotective effects. Also, the HDACi down regulates the pro-inflammatory cytokines (IL-6 and TNF- decreasing the neurotoxicity. HDACi can also avoid and prevent the entrance of the virus into the Central nervous System (CNS) as well as decrease the virus replication by downregulating the virus receptors. Here we review the mechanisms that could explain how the SARS-CoV-2 virus could reach the CNS, induce the neurological damage and symptoms, as well as the possibility to use HDACi as neuroprotective therapy.