The next generation of cellular technology, 6G, is being developed to enable a wide range of new applications and services for the Internet of Things (IoT). One of 6G's main advantages for IoT applications is its ability to support much higher data rates and bandwidth as well as to support ultra-low latency. However, with this increased connectivity will come to an increased risk of cyber threats, as attackers will be able to exploit the large network of connected devices. Generative Artificial Intelligence (AI) can be used to detect and prevent cyber attacks by continuously learning and adapting to new threats and vulnerabilities. In this paper, we discuss the use of generative AI for cyber threat-hunting (CTH) in 6G-enabled IoT networks. Then, we propose a new generative adversarial network (GAN) and Transformer-based model for CTH in 6G-enabled IoT Networks. The experimental analysis results with a new cyber security dataset demonstrate that the Transformer-based security model for CTH can detect IoT attacks with a high overall accuracy of 95%. We examine the challenges and opportunities and conclude by highlighting the potential of generative AI in enhancing the security of 6G-enabled IoT networks and call for further research to be conducted in this area.