Abstract: Understanding 3D cell shape is crucial in biomedical research, where morphology serves as a key indicator of disease, cellular state, and drug response. However, existing 3D point cloud classification models often lack interpretability, making it difficult to extract biologically meaningful insights. To address this, we propose PointMIL, an inherently interpretable point cloud classifier using Multiple Instance Learning (MIL). Unlike other methods that rely on global interpretations, PointMIL simultaneously improves accuracy of point cloud-based classifier backbones and provides fine-grained, point-specific explanations, pinpointing the most informative regions of 3D shapes, without requiring $\textit{post-hoc}$ analysis. We demonstrate PointMIL on two publicly available datasets of biological cells showing state-of-the-art mACC (97.3\%) and F1 (97.5\%) on the IntrA biomedical dataset. Additionally, we introduce a novel dataset of drug-treated cancer cells (Morph3DCell), to show PointMIL's ability to reveal the morphological effects of drug treatments at a fine-grained level, with implications for drug discovery and mechanism-of-action prediction. Beyond biomedical applications, we show that PointMIL also offers quality interpretations and improves the classification accuracy on standard shape benchmarks such as ModelNet40 and ScanObjectNN, demonstrating its generalisation to broader 3D object recognition tasks.