Background: This study explored vaccination hesitancy, diabetes-specific COVID-19 vaccination concerns, and whether they predicted vaccination uptake in people with diabetes. Methods: Quantitative, cross-sectional, and predictive approaches were used. An online survey was conducted with people with diabetes attending four Australian health services, using convenience sampling (n = 842). The survey data collected included clinico-demographic characteristics, COVID-19 vaccine hesitancy, and attitudes around COVID-19 vaccine confidence and complacency. Clinico-demographic characteristics that predicted vaccination status, vaccine hesitancy, and vaccine-related attitudes were identified using regression analyses. Results: Most participants received at least one COVID-19 vaccine dose. Younger age and type 1 diabetes were associated with lower vaccination status, and they were partially mediated through higher vaccine hesitancy. Younger age and English as a dominant language were associated with higher negative attitudes towards speed of vaccine development. Conclusions: Despite an overall high vaccination rate, general and diabetes-specific COVID-19 vaccine concerns are a barrier to uptake for some people with diabetes, particularly in those who are younger or have type 1 diabetes. A detailed understanding of concerns for particular subgroups can help tailor information to increase vaccine acceptance, particularly in the context of requiring booster doses.