The sustainable development of humanity imposes precise norms regarding the management of natural resources, their extraction, use, and the introduction in a complex, innovative circuit of the waste resulting from exploitation. The paper deals with some aspects related to the sustainable management of general medical waste on the one hand and the medical waste specific to the COVID-19 pandemic, on the other hand. Medical waste requires special treatment given its impact on the environment and on humanity. The management of activities related to its storage, transport, destruction is an important point in the sustainable development of mankind, especially in the current context of the pandemic. Medical waste is in a continuous increase in quantity and involves many effects in various activity fields. Through a scientometric study in the Web of Science—WOS database, the authors identify clusters of keywords, analyze the articles identified in the WOS and identify the main research directions and existing concepts. Corroborating and interpreting the results obtained, three significant trends of approach to medical waste are identified: M—management (1); E—exposure (2); and D—distribution (3). An extensive map of the concepts is made, a narrow map of the concepts used, and a theoretical map of the concepts. The link between medical waste and the development of a sustainable society is demonstrated, and it is possible to open new research directions. The scientometric research undertaken on 1192 WOS articles that were published in 2020 led to the selection of 32, focused on issues related to hazardous medical waste, especially of COVID-19 patients. Following this approach, the authors were able to see, by comparison, the different forms of management of this waste in different countries, thus being able to contribute to the creation of procedures for the collection, storage, and destruction of this hazardous waste, with direct influence on the environment.