This paper introduces AIDetx, a novel method for detecting machine-generated text using data compression techniques. Traditional approaches, such as deep learning classifiers, often suffer from high computational costs and limited interpretability. To address these limitations, we propose a compression-based classification framework that leverages finite-context models (FCMs). AIDetx constructs distinct compression models for human-written and AI-generated text, classifying new inputs based on which model achieves a higher compression ratio. We evaluated AIDetx on two benchmark datasets, achieving F1 scores exceeding 97% and 99%, respectively, highlighting its high accuracy. Compared to current methods, such as large language models (LLMs), AIDetx offers a more interpretable and computationally efficient solution, significantly reducing both training time and hardware requirements (e.g., no GPUs needed). The full implementation is publicly available at https://github.com/AIDetx/AIDetx.