Out-of-distribution (OoD) detection techniques for deep neural networks (DNNs) become crucial thanks to their filtering of abnormal inputs, especially when DNNs are used in safety-critical applications and interact with an open and dynamic environment. Nevertheless, integrating OoD detection into state-of-the-art (SOTA) object detection DNNs poses significant challenges, partly due to the complexity introduced by the SOTA OoD construction methods, which require the modification of DNN architecture and the introduction of complex loss functions. This paper proposes a simple, yet surprisingly effective, method that requires neither retraining nor architectural change in object detection DNN, called Box Abstraction-based Monitors (BAM). The novelty of BAM stems from using a finite union of convex box abstractions to capture the learned features of objects for in-distribution (ID) data, and an important observation that features from OoD data are more likely to fall outside of these boxes. The union of convex regions within the feature space allows the formation of non-convex and interpretable decision boundaries, overcoming the limitations of VOS-like detectors without sacrificing real-time performance. Experiments integrating BAM into Faster R-CNN-based object detection DNNs demonstrate a considerably improved performance against SOTA OoD detection techniques.