Numerous viruses use specialized surface molecules called fusogens to enter host cells. Many of these viruses, including the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), can infect the brain and are associated with severe neurological symptoms through poorly understood mechanisms. We show that SARS-CoV-2 infection induces fusion between neurons and between neurons and glia in mouse and human brain organoids. We reveal that this is caused by the viral fusogen, as it is fully mimicked by the expression of the SARS-CoV-2 spike (S) protein or the unrelated fusogen p15 from the baboon orthoreovirus. We demonstrate that neuronal fusion is a progressive event, leads to the formation of multicellular syncytia, and causes the spread of large molecules and organelles. Last, using Ca2+ imaging, we show that fusion severely compromises neuronal activity. These results provide mechanistic insights into how SARS-CoV-2 and other viruses affect the nervous system, alter its function, and cause neuropathology.