In object detection, the detection backbone consumes more than half of the overall inference cost. Recent researches attempt to reduce this cost by optimizing the backbone architecture with the help of Neural Architecture Search (NAS). However, existing NAS methods for object detection require hundreds to thousands of GPU hours of searching, making them impractical in fast-paced research and development. In this work, we propose a novel zero-shot NAS method to address this issue. The proposed method, named MAE-DET, automatically designs efficient detection backbones via the Maximum Entropy Principle without training network parameters, reducing the architecture design cost to nearly zero yet delivering the state-of-the-art (SOTA) performance. Under the hood, MAE-DET maximizes the differential entropy of detection backbones, leading to a better feature extractor for object detection under the same computational budgets. After merely one GPU day of fully automatic design, MAE-DET innovates SOTA detection backbones on multiple detection benchmark datasets with little human intervention. Comparing to ResNet-50 backbone, MAE-DET is $+2.0\%$ better in mAP when using the same amount of FLOPs/parameters, and is $1.54$ times faster on NVIDIA V100 at the same mAP. Code and pre-trained models are available here (https://github.com/alibaba/lightweight-neural-architecture-search).