With the rapid rise of the Internet of Things (IoT), ensuring the security of IoT devices has become essential. One of the primary challenges in this field is that new types of attacks often have significantly fewer samples than more common attacks, leading to unbalanced datasets. Existing research on detecting intrusions in these unbalanced labeled datasets primarily employs Convolutional Neural Networks (CNNs) or conventional Machine Learning (ML) models, which result in incomplete detection, especially for new attacks. To handle these challenges, we suggest a new approach to IoT intrusion detection using Self-Supervised Learning (SSL) with a Markov Graph Convolutional Network (MarkovGCN). Graph learning excels at modeling complex relationships within data, while SSL mitigates the issue of limited labeled data for emerging attacks. Our approach leverages the inherent structure of IoT networks to pre-train a GCN, which is then fine-tuned for the intrusion detection task. The integration of Markov chains in GCN uncovers network structures and enriches node and edge features with contextual information. Experimental results demonstrate that our approach significantly improves detection accuracy and robustness compared to conventional supervised learning methods. Using the EdgeIIoT-set dataset, we attained an accuracy of 98.68\%, a precision of 98.18%, a recall of 98.35%, and an F1-Score of 98.40%.