Generative AI (GenAI) is driving the intelligence of wireless communications. Due to data limitations, random generation, and dynamic environments, GenAI may generate channel information or optimization strategies that violate physical laws or deviate from actual real-world requirements. We refer to this phenomenon as wireless hallucination, which results in invalid channel information, spectrum wastage, and low communication reliability but remains underexplored. To address this gap, this article provides a comprehensive concept of wireless hallucinations in GenAI-driven communications, focusing on hallucination mitigation. Specifically, we first introduce the fundamental, analyze its causes based on the GenAI workflow, and propose mitigation solutions at the data, model, and post-generation levels. Then, we systematically examines representative hallucination scenarios in GenAI-enabled communications and their corresponding solutions. Finally, we propose a novel integrated mitigation solution for GenAI-based channel estimation. At the data level, we establish a channel estimation hallucination dataset and employ generative adversarial networks (GANs)-based data augmentation. Additionally, we incorporate attention mechanisms and large language models (LLMs) to enhance both training and inference performance. Experimental results demonstrate that the proposed hybrid solutions reduce the normalized mean square error (NMSE) by 0.19, effectively reducing wireless hallucinations.