The exponential rise of healthcare problems like human aging and road traffic accidents have developed an intrinsic challenge to biomedical sectors concerning the arrangement of patient-specific biomedical products. The additively manufactured implants and scaffolds have captured global attention over the last two decades concerning their printing quality and ease of manufacturing. However, the inherent challenges associated with additive manufacturing (AM) technologies, namely process selection, level of complexity, printing speed, resolution, biomaterial choice, and consumed energy, still pose several limitations on their use. Recently, the whole world has faced severe supply chain disruptions of personal protective equipment and basic medical facilities due to a respiratory disease known as the coronavirus (COVID-19). In this regard, local and global AM manufacturers have printed biomedical products to level the supply–demand equation. The potential of AM technologies for biomedical applications before, during, and post-COVID-19 pandemic alongwith its relation to the industry 4.0 (I4.0) concept is discussed herein. Moreover, additive manufacturing technologies are studied in this work concerning their working principle, classification, materials, processing variables, output responses, merits, challenges, and biomedical applications. Different factors affecting the sustainable performance in AM for biomedical applications are discussed with more focus on the comparative examination of consumed energy to determine which process is more sustainable. The recent advancements in the field like 4D printing and 5D printing are useful for the successful implementation of I4.0 to combat any future pandemic scenario. The potential of hybrid printing, multi-materials printing, and printing with smart materials, has been identified as hot research areas to produce scaffolds and implants in regenerative medicine, tissue engineering, and orthopedic implants.