The current COVID-19 pandemic has created unmeasurable damages to society at a global level, from the irreplaceable loss of life, to the massive economic losses. In addition, the disease threatens further biodiversity loss. Due to their shared physiology with humans, primates, and particularly great apes, are susceptible to the disease. However, it is still uncertain how their populations would respond in case of infection. Here, we combine stochastic population and epidemiological models to simulate the range of potential effects of COVID-19 on the probability of extinction of mountain gorillas. We find that extinction is sharply driven by increases in the basic reproductive number and that the probability of extinction is greatly exacerbated if the immunity lasts less than 6 months. These results stress the need to limit exposure of the mountain gorilla population, the park personnel and visitors, as well as the potential of vaccination campaigns to extend the immunity duration.