The application of Large Language Models (LLMs) in healthcare raises concerns about linguistic justice and health equity, as disparities in data availability across languages during training and evaluation cause significant performance variations that risk reinforcing existing inequities in healthcare access and outcomes. The study outlines strategies for integrating linguistic justice into LLM assessment frameworks to advance health equity and global health. Multilingualism better achieves linguistic justice than monolingualism in English or dominant national languages, yet linguistic and cultural biases embedded in LLMs risk exacerbating health inequities, particularly for marginalized populations. Significant disparities exist in natural language text availability across linguistic groups in corpora used for LLM training. The ROOTS corpus comprises 46 natural languages, with English (30.03%), Simplified Chinese (16.16%), French (12.9%), and Spanish (10.85%) collectively constituting 68% of the entire corpus. The Multilingual Medical Corpus (MMedC) contains 25.5 billion tokens across six major languages: English (41.4%), Chinese (18.6%), French (17.1%), Spanish (8.0%), Russian (7.5%), and Japanese (6.6%). This data disparity leads to discrepancies in LLM foundational capabilities across linguistic contexts, raising concerns over linguistic inequities that may propagate through downstream applications. Due to limited training data for low-resource languages, LLMs often exhibit suboptimal performance when processing such languages.