This paper proposes a novel universal quantile regression approach for solving a multi-product inventory management problem, leveraging the in-context learning (ICL) capability of time-series transformers. Our work not only provides a new meta-learning approach for multi-product inventory management, but also extends the state-of-the-art in ICL of transformers by showing how they can be used as universal quantile regressors for data that is not i.i.d. In numerical experiments using a large real-world dataset, our meta-learner consistently outperforms state-of-the-art benchmark models. Remarkably, it outperforms task-specific benchmarks, even when applied to new, unseen inventory management tasks.