Background: The recent human monkeypox virus (HMPXV) outbreak in non-endemic countries that started in May 2022 has raised concerns among public health authorities worldwide. Healthcare workers (HCWs) play a decisive role during epidemics in transmitting accurate information to the public and motivating them to pursue protective behaviours, including immunisation. Methods: A cross-sectional survey-based study was conducted in the Czech Republic in September 2022 to evaluate HMPXV-related knowledge and vaccination perceptions among HCWs. The study utilised a digital self-administered questionnaire (SAQ) to collect data from the target population. The proposed SAQ inquired about participants’ sociodemographic and anamnestic characteristics, perceived knowledge of HMPXV, factual knowledge, and vaccination perceptions according to the health belief model (HBM). Results: A total of 341 participants were included in this study; most of them were females (88.9%), allied HCWs (89.4%), heterosexuals (87.1%), married (61.9%), and vaccinated against COVID-19 (91.2%). Only 8.8% of the participants agreed to receive vaccination against HMPXV; 44.9% rejected it, while 46.3% were hesitant. While digital news portals (47.5%) and social media (25.8%) were among the most utilised sources of information about HMPXV, the scientific journals (5.6%), ECDC (5%), and the U.S. CDC (1.5%) were the least common sources. The participants demonstrated suboptimal levels of factual knowledge, especially regarding HMPXV vaccines (1.5 ± 1.2 (0–4)) and treatments (0.9 ± 0.9 (0–4)). Additionally, several misconceptions were detectable among the participants, regarding topics such as the availability of effective vaccines and antivirals against HMPXV, the risk of vertical transmission, and homosexual stigmatisation. The HBM indicated that the cues to action and perceived susceptibility were the most important constructs to predict HMPXV vaccine acceptance. Conclusions: the findings of this study call upon public health practitioners and health policymakers in the Czech Republic to act accordingly in order to determine the drivers of vaccine hesitancy among Czech HCWs. Dedicated educational campaigns should aim to counter the HCWs’ misconceptions around HMPXV, and future studies should aim to explore the prevalence and drivers of HMPXV vaccine hesitancy among the general population.