With ongoing climate change, which alters the conditions for pathogens and vectors, zoonotic diseases such as monkeypox virus will become a challenge and a great threat impacting global health in future decades. A current outbreak of monkeypox is occurring in over 125 countries, with a report of thousands of cases in countries where this virus has never appeared. Occupational exposure to the monkeypox virus has recently been identified as an issue of major concern for occupational health, especially in healthcare settings. A scoping review following the PRISMA guidelines was performed, aiming to analyze the effects that the current monkeypox outbreak has in workplaces, given the potential exposure of healthcare workers to the virus, the possible spread of the virus in occupational settings, and the preventive measures that are necessary to implement. At the end of the selection process, 21 studies were included in the review. Healthcare workers are considered at a high risk, and similar preventive measures to those adopted during the SARS-CoV-2 pandemic must be implemented in all healthcare settings. The main recommendations for preventing and managing monkeypox in occupational settings are the vaccination of exposed workers, the prompt identification and isolation of infected individuals, and good hygiene practices. Education and specific training are necessary in non-endemic countries to make healthcare workers able to recognize the disease and prevent further contagions. Although monkeypox seems unlikely to reach the pandemic spread of COVID-19, an approach to global health even to avoid future zoonotic epidemics is required by all stakeholders.