Recently, learning effective representations of urban regions has gained significant attention as a key approach to understanding urban dynamics and advancing smarter cities. Existing approaches have demonstrated the potential of leveraging mobility data to generate latent representations, providing valuable insights into the intrinsic characteristics of urban areas. However, incorporating the temporal dynamics and detailed semantics inherent in human mobility patterns remains underexplored. To address this gap, we propose a novel urban region representation learning model, Mobility Time Series Contrastive Learning for Urban Region Representations (MobiCLR), designed to capture semantically meaningful embeddings from inflow and outflow mobility patterns. MobiCLR uses contrastive learning to enhance the discriminative power of its representations, applying an instance-wise contrastive loss to capture distinct flow-specific characteristics. Additionally, we develop a regularizer to align output features with these flow-specific representations, enabling a more comprehensive understanding of mobility dynamics. To validate our model, we conduct extensive experiments in Chicago, New York, and Washington, D.C. to predict income, educational attainment, and social vulnerability. The results demonstrate that our model outperforms state-of-the-art models.