Monocular 3D object detection is an important challenging task in autonomous driving. Existing methods mainly focused on performing 3D detection in ideal weather conditions, characterized by scenarios with clear and optimal visibility. However, a challenge like autonomous driving requires the ability to handle changes in weather conditions (e.g., foggy), not just clear weather. To do this, we propose MonoWAD, a novel weather-robust monocular 3D object detector with a weather-adaptive diffusion model. We introduce two components: (1) the weather codebook to memorize the knowledge of the clear weather and generate a weather-reference feature for any input, and (2) the weather-adaptive diffusion model to enhance the feature representation of the input feature by incorporating a weather-reference feature. This serves an attention role in indicating how much improvement is needed for the input feature according to the weather conditions. For this purpose, we introduce weather-adaptive enhancement loss to enhance the feature representation under both clear and foggy weather conditions. Extensive experiments on monocular images under various weather conditions, MonoWAD achieves weather-robust monocular 3D object detection. Code and dataset will be released after the review process is over.