The spread of coronavirus disease 2019 (COVID-19) has affected both physical health and mental well-being around the world. Stress-related reactions, if prolonged, may result in mental health problems. We examined the consequences of the COVID-19 pandemic on mental health in a multinational study and explored the effects of government responses to the outbreak. We sampled 18,171 community adults from 35 countries/societies, stratified by age, gender, and region of residence. Across the 35 societies, 26.6% of participants reported moderate to extremely severe depression symptoms, 28.2% moderate to extremely severe anxiety symptoms, and 18.3% moderate to extremely severe stress symptoms. Coronavirus anxiety comprises two factors, namely Perceived Vulnerability and Threat Response. After controlling for age, gender, and education level, perceived vulnerability predicted higher levels of negative emotional symptoms and psychological distress, whereas threat response predicted higher levels of self-rated health and subjective well-being. People in societies with more stringent control policies had more threat response and reported better subjective health. Coronavirus anxiety exerts detrimental effects on subjective health and well-being, but also has the adaptive function in mobilizing safety behaviors, providing support for an evolutionary perspective on psychological adaptation.