The multiple-input multiple-output (MIMO) receiver processing is a key technology for current and next-generation wireless communications. However, it faces significant challenges related to complexity and scalability as the number of antennas increases. Artificial intelligence (AI), a cornerstone of next-generation wireless networks, offers considerable potential for addressing these challenges. This paper proposes an AI-driven, universal MIMO receiver architecture based on Markov chain Monte Carlo (MCMC) techniques. Unlike existing AI-based methods that treat receiver processing as a black box, our MCMC-based approach functions as a generic Bayesian computing engine applicable to various processing tasks, including channel estimation, symbol detection, and channel decoding. This method enhances the interpretability, scalability, and flexibility of receivers in diverse scenarios. Furthermore, the proposed approach integrates these tasks into a unified probabilistic framework, thereby enabling overall performance optimization. This unified framework can also be seamlessly combined with data-driven learning methods to facilitate the development of fully intelligent communication receivers.