In this paper, we propose a new black-box explainability algorithm and tool, YO-ReX, for efficient explanation of the outputs of object detectors. The new algorithm computes explanations for all objects detected in the image simultaneously. Hence, compared to the baseline, the new algorithm reduces the number of queries by a factor of 10X for the case of ten detected objects. The speedup increases further with with the number of objects. Our experimental results demonstrate that YO-ReX can explain the outputs of YOLO with a negligible overhead over the running time of YOLO. We also demonstrate similar results for explaining SSD and Faster R-CNN. The speedup is achieved by avoiding backtracking by combining aggressive pruning with a causal analysis.