Growing urbanization and the related demand for resources together with the climate change appear to be among the factors responsible for the intensified frequency and severity of disasters worldwide. At the same time, urbanization is related not only with the increasing flow of inhabitants to the big cities but also with an increase in the number of pet ownership in seeking social, psychological and health benefits. But when a disaster strikes, companion animals are affected as much as humans. Their survival depends on the preliminary preparedness of their guardians for disaster response and recovery. For this purpose, the present study investigated the level of disaster preparedness among 335 pet owners in Bulgaria through an anonymous written questionnaire. The results showed that 64.86% of the participants in the survey were women, 52.24% of all respondents were 19–24 years old and 75.45% were keeping pets at the moment of filling in the survey. The study found that 87.16% of the respondents were well-informed about the likelihood of disaster hazards in their residential area. Pet owners were prepared to approach the relevant public health authorities (89.55% of them), respectively the animal health services (82.88%) in case of emergency. Only 36.72% of all pet keepers had a prepared disaster family plan, with another 28.96% of the respondents having developed a disaster pet action plan for their animal companions. If emergency evacuation is needed, more than 66% of the respondents would take their pets with them during relocation. This intention was statistically significant in women and those pet owners who were familiar with the potential disaster hazards.