This research addresses public speculation that SARS-CoV-2 might be transmitted by mosquitoes. The World Health Organization has stated "To date there has been no information nor evidence to suggest that the new coronavirus could be transmitted by mosquitoes". Here we provide the first experimental data to investigate the capacity of SARS-CoV-2 to infect and be transmitted by mosquitoes. Three widely distributed species of mosquito; Aedes aegypti, Ae. albopictus and Culex quinquefasciatus, representing the two most significant genera of arbovirus vectors that infect people, were tested. We demonstrate that even under extreme conditions, SARS-CoV-2 virus is unable to replicate in these mosquitoes and therefore cannot be transmitted to people even in the unlikely event that a mosquito fed upon a viremic host.