By integrating Artificial Intelligence (AI) with the Internet of Things (IoT), Artificial Intelligence of Things (AIoT) has revolutionized many fields. However, AIoT is facing the challenges of energy consumption and carbon emissions due to the continuous advancement of mobile technology. Fortunately, Generative AI (GAI) holds immense potential to reduce carbon emissions of AIoT due to its excellent reasoning and generation capabilities. In this article, we explore the potential of GAI for carbon emissions reduction and propose a novel GAI-enabled solution for low-carbon AIoT. Specifically, we first study the main impacts that cause carbon emissions in AIoT, and then introduce GAI techniques and their relations to carbon emissions. We then explore the application prospects of GAI in low-carbon AIoT, focusing on how GAI can reduce carbon emissions of network components. Subsequently, we propose a Large Language Model (LLM)-enabled carbon emission optimization framework, in which we design pluggable LLM and Retrieval Augmented Generation (RAG) modules to generate more accurate and reliable optimization problems. Furthermore, we utilize Generative Diffusion Models (GDMs) to identify optimal strategies for carbon emission reduction. Simulation results demonstrate the effectiveness of the proposed framework. Finally, we insightfully provide open research directions for low-carbon AIoT.