To be adopted in safety-critical domains like medical image analysis, AI systems must provide human-interpretable decisions. Variational Information Pursuit (V-IP) offers an interpretable-by-design framework by sequentially querying input images for human-understandable concepts, using their presence or absence to make predictions. However, existing V-IP methods overlook sample-specific uncertainty in concept predictions, which can arise from ambiguous features or model limitations, leading to suboptimal query selection and reduced robustness. In this paper, we propose an interpretable and uncertainty-aware framework for medical imaging that addresses these limitations by accounting for upstream uncertainties in concept-based, interpretable-by-design models. Specifically, we introduce two uncertainty-aware models, EUAV-IP and IUAV-IP, that integrate uncertainty estimates into the V-IP querying process to prioritize more reliable concepts per sample. EUAV-IP skips uncertain concepts via masking, while IUAV-IP incorporates uncertainty into query selection implicitly for more informed and clinically aligned decisions. Our approach allows models to make reliable decisions based on a subset of concepts tailored to each individual sample, without human intervention, while maintaining overall interpretability. We evaluate our methods on five medical imaging datasets across four modalities: dermoscopy, X-ray, ultrasound, and blood cell imaging. The proposed IUAV-IP model achieves state-of-the-art accuracy among interpretable-by-design approaches on four of the five datasets, and generates more concise explanations by selecting fewer yet more informative concepts. These advances enable more reliable and clinically meaningful outcomes, enhancing model trustworthiness and supporting safer AI deployment in healthcare.