In August 2020 as Texas was coming down from a summer COVID-19 surge, forecasts suggested that Hurricane Laura was tracking towards 6M residents along the East Texas coastline threatening to spread COVID-19 across the state. To assist local authorities facing the dual threat, we developed a framework that integrates evacuation dynamics and local pandemic conditions to quantify COVID-19 importations due to hurricane evacuations. For Hurricane Laura, we estimate that 499,500 [90% Credible Interval (CI): 347,500, 624,000] people evacuated the Texan counties, and that there were 2,900 [90% CI: 1,700, 5,800] importations of COVID-19 across the state. To demonstrate the transferability of the framework, we apply it to a scenario with characteristics matching those of Hurricane Rita, where a much feared direct hit towards the highly populated Houston/Galveston area was forecasted. For this scenario we estimate 1,054,500 evacuations [90% CI: 832,500, 1,162,000], and 6,850 COVID-19 importations [90% CI: 4,100, 13,670]. Overall, we present a flexible and transferable framework that captures spatial heterogeneity and incorporates geographic components for anticipating potential epidemiological risks resulting from evacuation movement due to hurricane events.