Healthcare workers are particularly exposed to biological risk during their daily occupational activities. Nowadays, severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has become one of the most widespread infectious agents. In the current study, we performed a survey on the attitude and behavior of Polish healthcare workers (HCW), which comprise physicians (MD) and administrative healthcare assistants (HA) towards the Coronavirus Disease 2019 (COVID-19) vaccination. Our study involved 2300 subjects (42.17% female; 10.96% MD; 5.87% HA). The evaluation was conducted using a Google Forms survey based on original questions and the Depression, Anxiety and Stress Scale-21 Items questionnaire. HCW significantly more often demonstrated their willingness to get vaccinated against the SARS-CoV-2 as compared to the control group (82.95% vs. 54.31%, respectively). The main concern, as regards all groups, was the development of long-term side effects after getting COVID-19 vaccine. The study revealed that depression significantly affects the willingness to get vaccinated. The readiness was significantly strengthened by positive medical history of recommended vaccinations, fear of catching COVID-19, as well as fear of passing on the disease to the relatives. Overall, the percentage of HCW, who want to be vaccinated against COVID-19 remains unsatisfactory. Further works exploring this subject are needed to take a step closer to achieving the herd immunity in the era of the COVID-19 pandemic.