In December 2019, a pneumonia outbreak was reported in Wuhan, Hubei province, China. Since then, the World Health Organization declared a public health emergency of international concern due to a growing number of deaths around the globe, as well as unparalleled economic and sociodemographic consequences. The disease called coronavirus disease 2019 (COVID-19) is caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), a novel form of human coronavirus. Although coronavirus infections have been associated with neurological manifestations such as febrile seizures, convulsions, change in mental status, and encephalitis, less is known about the impact of SARS-CoV-2 in the brain. Recently, emerging evidence suggests that SARS-CoV-2 is associated with neurological alterations in COVID-19 patients with severe clinical manifestations. The molecular and cellular mechanisms involved in this process, as well as the neurotropic and neuroinvasive properties of SARS-CoV-2, are still poorly understood. Glial cells, such as astrocytes and microglia, play pivotal roles in the brain response to neuroinflammatory insults and neurodegenerative diseases. Further, accumulating evidence has shown that those cells are targets of several neurotropic viruses that severely impact their function. Glial cell dysfunctions have been associated with several neuroinflammatory diseases, suggesting that SARS-CoV-2 likely has a primary effect on these cells in addition to a secondary effect from neuronal damage. Here, we provide an overview of these data and discuss the possible implications of glial cells as targets of SARS-CoV-2. Considering the roles of microglia and astrocytes in brain inflammatory responses, we shed light on glial cells as possible drivers and potential targets of therapeutic strategies against neurological manifestations in patients with COVID-19. The main goal of this review is to highlight the need to consider glial involvement in the progression of COVID-19 and potentially include astrocytes and microglia as mediators of SARS-CoV-2-induced neurological damage.