Accurately predicting blood glucose (BG) levels of ICU patients is critical, as both hypoglycemia (BG < 70 mg/dL) and hyperglycemia (BG > 180 mg/dL) are associated with increased morbidity and mortality. This study presents a proof-of-concept machine learning framework, the Multi-source Irregular Time-Series Transformer (MITST), designed to predict BG levels in ICU patients. In contrast to existing methods that rely heavily on manual feature engineering or utilize limited Electronic Health Record (EHR) data sources, MITST integrates diverse clinical data--including laboratory results, medications, and vital signs without predefined aggregation. The model leverages a hierarchical Transformer architecture, designed to capture interactions among features within individual timestamps, temporal dependencies across different timestamps, and semantic relationships across multiple data sources. Evaluated using the extensive eICU database (200,859 ICU stays across 208 hospitals), MITST achieves a statistically significant ( p < 0.001 ) average improvement of 1.7 percentage points (pp) in AUROC and 1.8 pp in AUPRC over a state-of-the-art random forest baseline. Crucially, for hypoglycemia--a rare but life-threatening condition--MITST increases sensitivity by 7.2 pp, potentially enabling hundreds of earlier interventions across ICU populations. The flexible architecture of MITST allows seamless integration of new data sources without retraining the entire model, enhancing its adaptability for clinical decision support. While this study focuses on predicting BG levels, we also demonstrate MITST's ability to generalize to a distinct clinical task (in-hospital mortality prediction), highlighting its potential for broader applicability in ICU settings. MITST thus offers a robust and extensible solution for analyzing complex, multi-source, irregular time-series data.