Recently, the diffusion model has emerged as a superior generative model that can produce high-quality images with excellent realism. There is a growing interest in applying diffusion models to image translation tasks. However, for medical image translation, the existing diffusion models are deficient in accurately retaining structural information since the structure details of source domain images are lost during the forward diffusion process and cannot be fully recovered through learned reverse diffusion, while the integrity of anatomical structures is extremely important in medical images. Training and conditioning diffusion models using paired source and target images with matching anatomy can help. However, such paired data are very difficult and costly to obtain, and may also reduce the robustness of the developed model to out-of-distribution testing data. We propose a frequency-guided diffusion model (FGDM) that employs frequency-domain filters to guide the diffusion model for structure-preserving image translation. Based on its design, FGDM allows zero-shot learning, as it can be trained solely on the data from the target domain, and used directly for source-to-target domain translation without any exposure to the source-domain data during training. We trained FGDM solely on the head-and-neck CT data, and evaluated it on both head-and-neck and lung cone-beam CT (CBCT)-to-CT translation tasks. FGDM outperformed the state-of-the-art methods (GAN-based, VAE-based, and diffusion-based) in all metrics, showing its significant advantages in zero-shot medical image translation.