Accurate outcome prediction for head and neck cancer is critical but remains challenging due to domain shifts across multi-institutional imaging datasets. Existing domain generalization (DG) methods focus on visual features while overlooking clinical domain-invariant information. To address this gap, we propose MedPro-DG, a novel prompt learning framework that integrates CT imaging with clinical variables using domain-aware masked contrastive prompt learning. Our method can effectively mitigate domain shifts by aligning cross-modal features with domain-invariant clinical semantics. Extensive experiments conducted across six medical centers demonstrate the superiority of MedPro-DG, which outperforms state-of-the-art DG methods by 1.35% in AUC and 4.06% in ACC on average. Ablation studies further reveal that our prompt learning can capture clinically domain-invariant features, highlighting their diagnostic relevance. This work pioneers domain-invariant vision-language fusion for medical domain generalization, providing an available and effective solution for multi-center collaborative diagnosis.