The purpose of this study was to investigate mental health problems among international students in South Korean universities during the COVID-19 pandemic, as well as to identify the factors that affect their mental health. A total of 488 international students living in South Korea participated in a web-based survey. The questionnaire was created using the Google Forms platform, and a link to the questionnaire was shared through social media. Multiple logistic regression analysis was conducted to analyze the data. The prevalence rates of sleep problems, anxiety, and depression among international students were 47.1%, 39.6%, and 49%, respectively. The prevalence of mental health problems was higher among participants who were male, living with someone, residents of a rural area, and earning a higher income. The following variables were found to contribute to the prevalence of mental health problems: undergraduate student status, good understanding of the Korean language, longer hours of media usage, and experiences related to COVID-19 infection. A collaborative effort between the government and universities to manage the mental health of international students could promote the mental health of these students.