Anomaly detection in medical imaging is essential for identifying rare pathological conditions, particularly when annotated abnormal samples are limited. We propose a hybrid anomaly detection framework that integrates self-supervised representation learning with manifold-based density estimation, a combination that remains largely unexplored in this domain. Medical images are first embedded into a latent feature space using pretrained, potentially domain-specific, backbones. These representations are then refined via Mean Shift Density Enhancement (MSDE), an iterative manifold-shifting procedure that moves samples toward regions of higher likelihood. Anomaly scores are subsequently computed using Gaussian density estimation in a PCA-reduced latent space, where Mahalanobis distance measures deviation from the learned normal distribution. The framework follows a one-class learning paradigm and requires only normal samples for training. Extensive experiments on seven medical imaging datasets demonstrate state-of-the-art performance. MSDE achieves the highest AUC on four datasets and the highest Average Precision on five datasets, including near-perfect performance on brain tumor detection (0.981 AUC/AP). These results underscore the potential of the proposed framework as a scalable clinical decision-support tool for early disease detection, screening in low-label settings, and robust deployment across diverse imaging modalities.