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Childhood malnutrition remains a major public health concern in Nepal and other low-resource settings, while conventional case-finding approaches are labor-intensive and frequently unavailable in remote areas. This study provides the first comprehensive assessment of machine learning and deep learning methodologies for identifying malnutrition among children under five years of age in Nepal. We systematically compared 16 algorithms spanning deep learning, gradient boosting, and traditional machine learning families, using data from the Nepal Multiple Indicator Cluster Survey (MICS) 2019. A composite malnutrition indicator was constructed by integrating stunting, wasting, and underweight status, and model performance was evaluated using ten metrics, with emphasis on F1-score and recall to account for substantial class imbalance and the high cost of failing to detect malnourished children. Among all models, TabNet demonstrated the best performance, likely attributable to its attention-based architecture, and outperformed both support vector machine and AdaBoost classifiers. A consensus feature importance analysis identified maternal education, household wealth index, and child age as the primary predictors of malnutrition, followed by geographic characteristics, vaccination status, and meal frequency. Collectively, these results demonstrate a scalable, survey-based screening framework for identifying children at elevated risk of malnutrition and for guiding targeted nutritional interventions. The proposed approach supports Nepal's progress toward the Sustainable Development Goals and offers a transferable methodological template for similar low-resource settings globally.