Medical large language models hold promise for reducing healthcare disparities, yet Hindi remains severely underrepresented. While medical LLMs excel in high-resource languages, their performance degrades sharply in Hindi, particularly on Indian systems of medicine. We argue that robust cross-lingual medical transfer requires Hindi reasoning. To this end, we introduce HiMed, a Hindi reasoning medical corpus and benchmark suite covering both Western and Indian medicine. We further propose HiMed-8B, a Hindi-form medical reasoning LLM, through the design of decaying scaffolding reward. Extensive experiments demonstrate improvement in Hindi medical reasoning performance and reduction in the English--Hindi accuracy gap. Ablation studies validate the contribution of each training stage and reward component. All data and code are available on GitHub: https://github.com/FreedomIntelligence/HiMed.