The manufacturing industry has undergone numerous revolutions over the years, with a unanimous acceptance of the greater benefits of being sustainable. The present industrial wave—Industry 4.0—by using its enabling technologies and principles holds great potential to develop sustainable manufacturing paradigms which require balancing out the three fundamental elements —products, processes, and systems. Yet, numerous stakeholders, including industrial policy and decision makers, remain oblivious of such potential and requirements. Thus, this bibliometric study is aimed at presenting an overview of the broad field of research on the convergence of sustainable manufacturing and Industry 4.0 under the umbrella of “Sustainable Manufacturing 4.0”, which has yet to be developed. It includes the dissemination of original findings on pathways and practices of Industry 4.0 applied to the development of sustainable manufacturing, contributing a bibliometric structure of the literature on the aforementioned convergence to reveal how Industry 4.0 could be used to shift the manufacturing sector to a more sustainable-based state. An initial research agenda for this emerging area has accordingly been presented, which may pave the way for having a futuristic view on Sustainable Manufacturing 5.0 in the next industrial wave, i.e., Industry 5.0.