In healthcare, the integration of multimodal data is pivotal for developing comprehensive diagnostic and predictive models. However, managing missing data remains a significant challenge in real-world applications. We introduce MARIA (Multimodal Attention Resilient to Incomplete datA), a novel transformer-based deep learning model designed to address these challenges through an intermediate fusion strategy. Unlike conventional approaches that depend on imputation, MARIA utilizes a masked self-attention mechanism, which processes only the available data without generating synthetic values. This approach enables it to effectively handle incomplete datasets, enhancing robustness and minimizing biases introduced by imputation methods. We evaluated MARIA against 10 state-of-the-art machine learning and deep learning models across 8 diagnostic and prognostic tasks. The results demonstrate that MARIA outperforms existing methods in terms of performance and resilience to varying levels of data incompleteness, underscoring its potential for critical healthcare applications.