Prior works on physical adversarial camouflage against vehicle detectors mainly focus on the effectiveness and robustness of the attack. The current most successful methods optimize 3D vehicle texture at a pixel level. However, this results in conspicuous and attention-grabbing patterns in the generated camouflage, which humans can easily identify. To address this issue, we propose a Customizable and Natural Camouflage Attack (CNCA) method by leveraging an off-the-shelf pre-trained diffusion model. By sampling the optimal texture image from the diffusion model with a user-specific text prompt, our method can generate natural and customizable adversarial camouflage while maintaining high attack performance. With extensive experiments on the digital and physical worlds and user studies, the results demonstrate that our proposed method can generate significantly more natural-looking camouflage than the state-of-the-art baselines while achieving competitive attack performance.