Deep learning has revolutionised healthcare applications, achieving remarkable success in medical diagnosis and treatment prediction. However, the inherent opacity of these models presents significant challenges for clinical deployment, where interpretable explanations are crucial for patient trust and regulatory compliance. This paper presents a novel constraint-aware counterfactual explanation model for generating personalised dietary interventions in anaemia patients. Anaemia affects over 1.9 billion people globally, yet existing explainable AI methods fail to provide clinically feasible and culturally appropriate recommendations. We develop a causal machine learning approach that integrates Pearl's causal hierarchy with domain-specific constraints to produce interpretable “what-if” scenarios. Our model incorporates nutritional, cultural, and economic constraints through augmented Lagrangian optimisation, ensuring recommendations remain clinically feasible whilst maintaining semantic meaningfulness. Experimental results demonstrate superior performance compared to existing explainable AI methods, achieving 84.3% anaemia reversal rates (vs 71.8% best baseline), 89.1% counterfactual validity, and 4.2 interpretability scores. The model generates recommendations requiring an average of 2.3 dietary changes within cognitive load thresholds whilst maintaining \(O(n log n)\) computational complexity suitable for real-time clinical deployment. This work advances explainable AI in healthcare by demonstrating how domain-specific constraints can enhance both interpretability and clinical utility of counterfactual explanations for chronic disease management.