Detecting out-of-distribution (OOD) objects is indispensable for safely deploying object detectors in the wild. Although distance-based OOD detection methods have demonstrated promise in image classification, they remain largely unexplored in object-level OOD detection. This paper bridges the gap by proposing a distance-based framework for detecting OOD objects, which relies on the model-agnostic representation space and provides strong generality across different neural architectures. Our proposed framework SIREN contributes two novel components: (1) a representation learning component that uses a trainable loss function to shape the representations into a mixture of von Mises-Fisher (vMF) distributions on the unit hypersphere, and (2) a test-time OOD detection score leveraging the learned vMF distributions in a parametric or non-parametric way. SIREN achieves competitive performance on both the recent detection transformers and CNN-based models, improving the AUROC by a large margin compared to the previous best method. Code is publicly available at https://github.com/deeplearning-wisc/siren.