(1) Background: Risk perception is a key factor in motivating people to comply with preventive behaviors during the COVID-19 pandemic. Appropriate risk perception is important to enhance beliefs and promote emergency management response to public health events. (2) Objective: This study developed a public risk perception measurement method for social media data to understand the dynamic characteristics of risk perception and emotional expression during public health emergencies. (3) Methods: Utilizing text-mining techniques and deep-learning algorithms, risk perception was calculated from two dimensions (dread and unknown) as well as the emotional expression characteristics of 185,025 posts from 10 January 2020 to 20 March 2020 on Sina Weibo. We also analyzed the characteristics of risk perception at different stages of the crisis life cycle. Furthermore, drawing on arousal theory, we constructed dynamic response relationships between emotion type (angry, fearful, sad, positive, and neutral) and risk perceptions by a vector autoregressive (VAR) model. (4) Results: The results revealed that the public expresses significantly more dread words than unknown words in shaping the risk perception process. As for the characteristics of evolution, public risk perception had been at a high level since the outbreak stage, and there was a sudden increase and a gradual decrease in the level of public risk perception. We also found that there is a significant response relationship between positive emotion, angry emotion, and risk perception. (5) Conclusion: This study provides a theoretical basis for more targeted epidemic crisis interventions. It points out the need for health communication strategy makers to consider the public’s risk perception and emotional expression characteristics during public health emergencies.