Since the beginning of 2020, the COVID-19 pandemic has caused unprecedented global disruption with considerable impact on human activities. However, natural hazards and related disasters do not wait for SARS-CoV-2 to vanish, resulting in the emergence of many conflicting issues between earthquake emergency response actions and pandemic mitigation measures. In this study, these conflicting issues are highlighted through the cases of four earthquakes that struck Greece at different phases of the pandemic. The earthquake effects on the local population and on the natural environment and building stock form ideal conditions for local COVID-19 outbreaks in earthquake-affected communities. However, the implementation of response actions and mitigation measures in light of a multi-hazard approach to disaster risk reduction and disaster risk management has led not only to the maintenance of pre-existing low viral load in the earthquake-affected areas, but in some cases even to their reduction. This fact suggests that the applied measures are good practice and an important lesson for improving disaster management in the future. Taking into account the aforementioned, a series of actions are proposed for the effective management of the impact of a geological hazard in the midst of an evolving biological hazard with epidemiological characteristics similar to the COVID-19 pandemic.