As a global epidemic of the social media age, COVID-19 has also resulted in an ‘infodemic’, which means the uncontrolled spreading of false information about the health situation. Spreading of health information is a special intersection point of the freedom of speech, freedom of science, and the fundamental right to life and health. The paper analyses the European and Hungarian legal framework for health communication from multiple perspectives. Regulatory challenges and solutions differ for professional health communication, commercial communication and health communication by laypeople. As with all forms of misinformation, private regulations of platform operators have a significant regulatory role to play in relation to health disinformation. As a result of the analysis, the paper provides a detailed regulatory map that also covers private regulation solutions and explores the factors that need to be considered when designing a comprehensive future regulation.