Unsupervised anomaly detection in brain imaging is challenging. In this paper, we propose a self-supervised masked mesh learning for unsupervised anomaly detection in 3D cortical surfaces. Our framework leverages the intrinsic geometry of the cortical surface to learn a self-supervised representation that captures the underlying structure of the brain. We introduce a masked mesh convolutional neural network (MMN) that learns to predict masked regions of the cortical surface. By training the MMN on a large dataset of healthy subjects, we learn a representation that captures the normal variation in the cortical surface. We then use this representation to detect anomalies in unseen individuals by calculating anomaly scores based on the reconstruction error of the MMN. We evaluate our framework by training on population-scale dataset UKB and HCP-Aging and testing on two datasets of Alzheimer's disease patients ADNI and OASIS3. Our results show that our framework can detect anomalies in cortical thickness, cortical volume, and cortical sulcus features, which are known to be sensitive biomarkers for Alzheimer's disease. Our proposed framework provides a promising approach for unsupervised anomaly detection based on normative variation of cortical features.