Functional decomposition (FD) is essential for simplifying complex systems in engineering design but remains a resource-intensive task reliant on expert knowledge. Despite advances in artificial intelligence, the automation of FD remains underexplored. This study introduces the use of GPT-4o, enhanced with a proposed Monte Carlo tree search for functional decomposition (MCTS-FD) algorithm, to automate FD. The approach is evaluated qualitatively by comparing outputs with those of graduate engineering students and quantitatively by assessing metrics such as structural integrity and semantic accuracy. The results show that GPT-4o, enhanced by MCTS-FD, outperforms smaller models in error rates and graph connectivity, highlighting the potential of large language models to automate FD with human-like accuracy.