Accurate and effective government communication is essential for public health emergencies. To optimize the effectiveness of government crisis communication, this paper puts forward an analytical perspective of supply–demand matching based on the interaction between the government and the public. We investigate the stage characteristics and the topic evolutions of both government information supply and public information demand through combined statistical analysis, text mining, text coding and cluster analysis, using empirical data from the National Health Commission’s WeChat in China. A quantitative measure reflecting the public demand for government information supply is proposed. Result indicates that the government has provided a large amount of high-intensity epidemic-related information, with six major topics being the medical team, government actions, scientific protection knowledge, epidemic situation, high-level deployment and global cooperation. The public’s greatest information needs present different characteristics at different stages, with “scientific protection knowledge”, “government actions” and “medical teams” being the most needed in the outbreak stage, the control stage and the stable stage, respectively. The subject of oversupply is “medical team”, and the subject of short supply is “epidemic dynamics” and “science knowledge”. This paper provides important theoretical and practical value for improving the effectiveness of government communication in public health crises.