Probabilistic Face Embeddings (PFE) can improve face recognition performance in unconstrained scenarios by integrating data uncertainty into the feature representation. However, existing PFE methods tend to be over-confident in estimating uncertainty and is too slow to apply to large-scale face matching. This paper proposes a regularized probabilistic face embedding method to improve the robustness and speed of PFE. Specifically, the mutual likelihood score (MLS) metric used in PFE is simplified to speedup the matching of face feature pairs. Then, an output-constraint loss is proposed to penalize the variance of the uncertainty output, which can regularize the output of the neural network. In addition, an identification preserving loss is proposed to improve the discriminative of the MLS metric, and a multi-layer feature fusion module is proposed to improve the neural network's uncertainty estimation ability. Comprehensive experiments show that the proposed method can achieve comparable or better results in 9 benchmarks than the state-of-the-art methods, and can improve the performance of risk-controlled face recognition. The code of our work is publicly available in GitHub (https://github.com/KaenChan/ProbFace).