Students have been highly vulnerable to mental health issues during the COVID-19 pandemic, and researchers have shown that perceived stress and mental health problems have increased during the pandemic. The aim of this study was to reveal the prevalence of perceived stress and mental health among students during the pandemic and to explore predictors of stress levels. A cross-sectional study was conducted on a sample of 358 undergraduates from 14 universities in Turkey, including 200 female students (56%). The measurements used in the study were the Generalized Anxiety Disorder 7-item (GAD-7) scale, Patient Health Questionnaire (PHQ-8), Satisfaction with Life Scale (SWLS), Perception of COVID Impact on Student Well-Being (CI), Perceived Stress Scale (PSS-10), Physical Activity Scale (PA), and a sociodemographic survey. Students reported high perceived stress, mild generalized anxiety, and low satisfaction with life. More than half of the students met the diagnostic criteria of GAD (52%) and depression (63%). Female and physically inactive students had higher PSS-10 levels. A hierarchical linear regression model showed that after controlling for gender and negative CI, anxiety and physical inactivity significantly predicted high perceived stress. The study shows that students’ mental health during the pandemic is at high risk.