Understanding the COVID-19 vaccine hesitancy, such as who and why, is very crucial since a large-scale vaccine adoption remains as one of the most efficient methods of controlling the pandemic. Such an understanding also provides insights into designing successful vaccination campaigns for future pandemics. Unfortunately, there are many factors involving in deciding whether to take the vaccine, especially from the cultural point of view. To obtain these goals, we design a novel culture-aware machine learning (ML) model, based on our new data collection, for predicting vaccination willingness. We further analyze the most important features which contribute to the ML model's predictions using advanced AI explainers such as the Probabilistic Graphical Model (PGM) and Shapley Additive Explanations (SHAP). These analyses reveal the key factors that most likely impact the vaccine adoption decisions. Our findings show that Hispanic and African American are most likely impacted by cultural characteristics such as religions and ethnic affiliation, whereas the vaccine trust and approval influence the Asian communities the most. Our results also show that cultural characteristics, rumors, and political affiliation are associated with increased vaccine rejection.