Display omitted •SARS-CoV-2 infection of neural tissue is non-permissive.•SARS-CoV-2 infection can elicit inflammatory response and cell damage.•Increasing virus amount and incubation times do not elicit permissive infection.•Divergences in viral sequences may explain differences in neural cell infectivity. Coronavirus disease 2019 (COVID-19) was initially described as a viral infection of the respiratory tract. It is now known, however, that several other organs are affected, including the brain. Neurological manifestations such as stroke, encephalitis, and psychiatric conditions have been reported in COVID-19 patients, but the neurotropic potential of the virus is still debated. Herein, we sought to investigate SARS-CoV-2 infection in human neural cells. We demonstrated that SARS-CoV-2 infection of neural tissue is non-permissive, however, it can elicit inflammatory response and cell damage. These findings add to the hypothesis that most of the neural damage caused by SARS-CoV-2 infection is due to a systemic inflammation leading to indirect harmful effects on the central nervous system despite the absence of local viral replication.