Severe Acute Respiratory Syndrome Coronavirus-2 infection has been associated to neurological symptoms characteristic of long-lasting post-acute coronavirus disease. However, the complex mechanisms involved in these clinical manifestations are still unclear. Glial cells are key to inflammation and neurodegeneration in response to central nervous system infection. To investigate this pathway, induced pluripotent stem cells human astrocytes and human microglial HMC3 cells were infected with SARS-CoV-2. Astrocytes showed to be prone to infection, while HMC3 supported only marginal virus replication. A significant IFN-β response was induced in astrocytes, while both cell types showed some level of chemoattractant production. Interestingly, both glial cells showed signs of senescence and activation of the pro-inflammatory cGAS-STING pathway. To investigate if glial cells infection could impair the function of neuronal networks, primary rat cortical cultures seeded on multi-electrode arrays were used to monitor the electrical activity after exposure to SARS-CoV-2. Effective SARS-CoV-2 infection of the glia led to a major loss of synaptic connections, an increase expression and production of pro-inflammatory cytokines and chemokines, and an increase of DNA damage foci. Intriguingly, the pro-inflammatory response was cGAS-STING dependent. Finally, an antagonist of the cGAS-STING pathway was able to ameliorate the decrease in electrical activity early post-infection. These data point to SARS-CoV-2 infection of the glia as a culprit for neurological complications during COVID-19.