In-context learning (ICL), the remarkable ability to solve a task from only input exemplars, has commonly been assumed to be a unique hallmark of Transformer models. In this study, we demonstrate that multi-layer perceptrons (MLPs) can also learn in-context. Moreover, we find that MLPs, and the closely related MLP-Mixer models, learn in-context competitively with Transformers given the same compute budget. We further show that MLPs outperform Transformers on a subset of ICL tasks designed to test relational reasoning. These results suggest that in-context learning is not exclusive to Transformers and highlight the potential of exploring this phenomenon beyond attention-based architectures. In addition, MLPs' surprising success on relational tasks challenges prior assumptions about simple connectionist models. Altogether, our results endorse the broad trend that ``less inductive bias is better" and contribute to the growing interest in all-MLP alternatives to task-specific architectures.