In this letter, we design a federated contrastive learning (FedCL) framework aimed at supporting personalized semantic communication. Our FedCL enables collaborative training of local semantic encoders across multiple clients and a global semantic decoder owned by the base station. This framework supports heterogeneous semantic encoders since it does not require client-side model aggregation. Furthermore, to tackle the semantic imbalance issue arising from heterogeneous datasets across distributed clients, we employ contrastive learning to train a semantic centroid generator (SCG). This generator obtains representative global semantic centroids that exhibit intra-semantic compactness and inter-semantic separability. Consequently, it provides superior supervision for learning discriminative local semantic features. Additionally, we conduct theoretical analysis to quantify the convergence performance of FedCL. Simulation results verify the superiority of the proposed FedCL framework compared to other distributed learning benchmarks in terms of task performance and robustness under different numbers of clients and channel conditions, especially in low signal-to-noise ratio and highly heterogeneous data scenarios.