Subspace clustering aims to group data points that lie in a union of low-dimensional subspaces and finds wide application in computer vision, hyperspectral imaging, and recommendation systems. However, most existing methods assume fully observed data, limiting their effectiveness in real-world scenarios with missing entries. In this paper, we propose a contrastive self-supervised framework, Contrastive Subspace Clustering (CSC), designed for clustering incomplete data. CSC generates masked views of partially observed inputs and trains a deep neural network using a SimCLR-style contrastive loss to learn invariant embeddings. These embeddings are then clustered using sparse subspace clustering. Experiments on six benchmark datasets show that CSC consistently outperforms both classical and deep learning baselines, demonstrating strong robustness to missing data and scalability to large datasets.