Dense Retrieval~(DR) has achieved state-of-the-art first-stage ranking effectiveness. However, the efficiency of most existing DR models is limited by the large memory cost of storing dense vectors and the time-consuming nearest neighbor search~(NNS) in vector space. Therefore, we present RepCONC, a novel retrieval model that learns discrete Representations via CONstrained Clustering. RepCONC jointly trains dual-encoders and the Product Quantization~(PQ) method to learn discrete document representations and enables fast approximate NNS with compact indexes. It models quantization as a constrained clustering process, which requires the document embeddings to be uniformly clustered around the quantization centroids. We theoretically demonstrate that the uniform clustering constraint facilitates representation distinguishability. Extensive experiments show that RepCONC substantially outperforms a wide range of existing retrieval models in terms of retrieval effectiveness, memory efficiency, and time efficiency.