The need for medical image encryption is increasingly pronounced, for example, to safeguard the privacy of the patients' medical imaging data. In this article, a novel deep learning-based key generation network (DeepKeyGen) is proposed as a stream cipher generator to generate the private key, which can then be used for encrypting and decrypting of medical images. In DeepKeyGen, the generative adversarial network (GAN) is adopted as the learning network to generate the private key. Furthermore, the transformation domain (that represents the "style" of the private key to be generated) is designed to guide the learning network to realize the private key generation process. The goal of DeepKeyGen is to learn the mapping relationship of how to transfer the initial image to the private key. We evaluate DeepKeyGen using three data sets, namely, the Montgomery County chest X-ray data set, the Ultrasonic Brachial Plexus data set, and the BraTS18 data set. The evaluation findings and security analysis show that the proposed key generation network can achieve a high-level security in generating the private key.