Adequate support in maternity wards is decisive for breastfeeding outcomes during the first year of life. Quality improvement interventions require the identification of the factors influencing hospital benchmark indicators. Machine Learning (ML) models and post-hoc Explainable Artificial Intelligence (XAI) techniques allow accurate predictions and explaining them. This study aimed to predict exclusive breastfeeding during the in-hospital postpartum stay by ML algorithms and explain the ML model's behaviour to support decision making. The dataset included 2042 mothers giving birth in 18 hospitals in Eastern Spain. We obtained information on demographics, mothers' breastfeeding experiences, clinical variables, and participating hospitals' support conditions. The outcome variable was exclusive breastfeeding during the in-hospital postpartum stay. We tested algorithms from different ML families. To evaluate the ML models, we applied 10-fold stratified cross-validation. We used the following metrics: Area under curve receiver operating characteristic (ROC AUC), area under curve precision-recall (PR AUC), accuracy, and Brier score. After selecting the best fitting model, we calculated Shapley's additive values to assign weights to each predictor depending on its additive contribution to the outcome and to explain the predictions. The XGBoost algorithms showed the best metrics (ROC AUC = 0.78, PR AUC = 0.86, accuracy = 0.75, Brier = 0.17). The main predictors of the model included, in order of importance, the pacifier use, the degree of breastfeeding self-efficacy, the previous breastfeeding experience, the birth weight, the admission of the baby to a neonatal care unit after birth, the moment of the first skin-to-skin contact between mother and baby, and the Baby-Friendly Hospital Initiative accreditation of the hospital. Specific examples for linear and nonlinear relations between main predictors and the outcome and heterogeneity of effects are presented. Also, we describe diverse individual cases showing the variation of the prediction depending on individual characteristics. The ML model adequately predicted exclusive breastfeeding during the in-hospital stay. Our results pointed to opportunities for improving care related to support for specific mother's groups, defined by current and previous infant feeding experiences and clinical conditions of the newborns, and the participating hospitals' support conditions. Also, XAI techniques allowed identifying non-linearity relations and effect's heterogeneity, explaining specific cases' risk variations.