Unified multimodal large language models (MLLMs) aim to unify image understanding and image generation within a single framework, where a shared visual tokenizer serves as the sole interface that maps high-dimensional images into a limited token budget for downstream multimodal reasoning and synthesis. However, existing shared-token designs are largely architecture-driven and lack an explicit criterion for what information should be preserved to simultaneously support semantic abstraction and visual detail. In this paper, we adopt a capacity-constrained perspective, viewing the shared tokenizer as a compute-bounded learner whose finite representational budget should prioritize reusable structure over hard-to-exploit high-entropy variations and redundancy. Motivated by this view, we propose \textbf{\textit{InfoTok}}, an information-regularized tokenization mechanism grounded in the Information Bottleneck (IB) principle. InfoTok explicitly controls information flow from images to shared tokens to multimodal outputs by imposing mutual-information (MI) constraints that enforce a principled trade-off between compression and task relevance, while also encouraging cross-modal consistency. Because MI is intractable for high-dimensional visual representations, we instantiate InfoTok with practical, differentiable dependence estimators, including a variational IB formulation and a Hilbert Schmidt Independence Criterion (HSIC) based alternative. Integrated into three representative unified MLLMs without introducing any additional training data, InfoTok consistently improves both image understanding and generation performance. These results support information-regularized visual tokenization as a sound basis for token learning in unified MLLMs.