Corona Virus Disease (COVID-19), originating in Wuhan city of China, has spread whole world in a short time and radically affected the individuals’ and societies’ lives. Even though the countries implemented different strategies for outbreak, most of the world's population had to cope with restrictions, long-term quarantines, remote working and distance education. All these situations negatively affect people's anxiety levels. In this study, data (n = 226) are collected through a questionnaire surveys within the sample of undergraduate students, and the effect of mental well-being on anxiety caused by COVID-19 is investigated. The validity and reliability of the Warwick-Edinburgh mental well-being scale developed by Tennant et al. (2007) is tested with exploratory factor analysis and reliability analysis. The effects of functional, intrinsic and extrinsic well-being concepts on three different levels of anxiety related to COVID-19, namely general, health and economic anxieties, are examined by ordinal logistic regression analysis. Research results revealed that functional and intrinsic well-being have a significant negative effect on the general anxiety level. However, mental well-being dimensions are found to have insignificant effects on economic and health anxieties. This study focuses on young individuals and provides conclusive evidence to further researches on the negative effects of the pandemics on individual’s psychology.