Background Standard precautions are minimum infection control practices used to prevent the transmission of diseases and applied to all patient care. Nursing students are at high risk of exposure to occupational biologic hazards because they are obligated to provide care to patients admitted with unknown infection statuses. Compliance with standard precautions is an effective and efficient means of infection prevention. However, their compliance with standard precautions among nursing students is not known in Ethiopia. Therefore, this study aimed to assess compliance with standard precautions and associated factors among undergraduate BSc nursing students at governmental universities located in the Amhara Region, northwest Ethiopia. Methods An institutional-based cross-sectional study was conducted among undergraduate BSc nursing students at the governmental universities located in Amhara Region, northwest Ethiopia, from April 15 to May 15, 2021. A simple random sampling technique was used to select 423 samples. Descriptive statistics were presented in text, tables, and charts. Multicollinearity and model fitness were checked. All variables were entered into multivariable logistic regression and a P-value of < 0.05 was considered to identify statistically significant factors. Result Around 221 (53.4%) of the study participants were males. Good compliance of nursing students towards standard precautions was 56.3% (95% CI = 51.4–60.9), which is significantly associated with good knowledge (AOR = 2.52, 95% CI = 1.61–3.94), a perceived safe workplace climate (AOR = 2.15, 95% CI = 1.24–3.71), and training or seminars related to standard precautions in the last six months (AOR = 1.52, 95% CI = 1.01–2.29). Conclusion The overall compliance of nursing students with standard precautions was low, with nearly half of the nursing students failing to comply with standard precautions. The major factors associated with good compliance were good knowledge, a perceived safe workplace, and having seminars or training in the last six months. Training, enhancing knowledge, and creating a safe hospital environment are recommended to improve nursing students’ compliance with standard precautions.