Climate change is no longer a hypothetical problem in the Caribbean but a new reality to which regional public health systems must adapt. One of its significant impacts is the increased transmission of infectious diseases, such as dengue fever, which is endemic in the region, and the presence of the Aedes aegypti mosquito vector responsible for transmitting the disease. (1) Methods: To assess the association between climatic factors and human dengue virus infections in the Caribbean, we conducted a systematic review of published studies on MEDLINE and Web of Science databases according to Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) criteria. (2) Results: In total, 153 papers were identified, with 27 studies selected that met the inclusion criteria ranging from the northern and southern Caribbean. Rainfall/precipitation and vapor pressure had a strong positive association with dengue incidence, whereas the evidence for the impact of temperatures was mixed. (3) Conclusions: The interaction between climate and human dengue disease in the Caribbean is complex and influenced by multiple factors, including waste management, infrastructure risks, land use changes, and challenged public health systems. Thus, more detailed research is necessary to understand the complexity of dengue within the wider Caribbean and achieve better dengue disease management.