The outbreak of COVID-19, initially developed in China in early December 2019, has rapidly spread to other countries and represents a public health emergency of international concern. COVID-19 has caused great concern about respiratory symptoms, but it is worth noting that it can also affect the gastrointestinal tract. However, the data on pancreatic involvement during SARS-CoV-2 infection are limited. The prevalence and severity of pancreatic damage and acute pancreatitis, as well as its pathophysiology, are still under debate. Moreover, the possible implication of pancreatic damage as an apparent adverse effect of COVID-19 therapies or vaccines are issues that need to be addressed. Finally, the COVID-19 pandemic has generated delays and organizational consequences for pancreatic surgery, an element that represent indirect damage from COVID-19. This narrative review aims to summarize and analyze all the aspects of pancreatic involvement in COVID-19 patients, trying to establish the possible underlying mechanisms and scientific evidence supporting the association between COVID-19 and pancreatic disease.