Background The experience of extreme worry and self-doubt before taking a test can drastically hinder an individual’s ability to perform well and may lead to miserable. Studies about test anxiety and associated factors among first-year health science students in Ethiopia are limited. Therefore, this study is meant to provide essential data for future interventions. Objective To assess test anxiety and associated factors among first-year regular undergraduate health science students of the University of Gondar, northwest Ethiopia, 2019. Methods An institutional-based cross-sectional study with a stratified random sampling technique. Test anxiety was assessed using the Test Anxiety Questionnaire. Data were analyzed using Statistical Package for Social Science (SPSS) version 20. Bivariate and multivariate logistic regression analysis was performed. A P -value of less than 0.05 was considered statistically significant in the multivariate analysis, and the strength of association was measured using adjusted odds ratio at a 95% confidence interval. Results In this study, the prevalence of test anxiety was 54.7% (95% CI=49.40–60.20). The result revealed that fathers’ education of grade 9–12 (AOR=0.31, 95% CI=0.14–0.69), mothers’ education of grade 9–12 (AOR=2.43, 95% CI=1.07–5.47), psychological distress (AOR=8.37, 95% CI=4.29–16.39), the field of studies; midwifery (AOR=3.56, 95% CI=1.07–11.76), and medicine (AOR=6.79, 95% CI=1.64–28.22) were significantly associated with test anxiety at a P -value<0.05. Conclusion The study found that test anxiety is a major problem of first-year undergraduate health science students. Mothers’ education of grades 9–12, psychological distress, midwifery, and medical field of studies were risk factors of test anxiety, whereas fathers’ education of grade 9–12 was protective for test anxiety. This showed that an increment in the education of father and mother has a controversial effect on test anxiety. It can be reduced by providing suitable trainings for first-year health science students in dealing with factors causing test anxiety.