Background Vaccines are medical products with a short shelf life and are easily damaged by deviations in temperature from the recommended ranges. Vaccines lose their quality if the cold chain system is not properly managed. Cold chain management is still a major challenge in developing countries, including Ethiopia. Thus, this study aimed to assess vaccine cold chain management and associated factors at public health facilities and district health offices. Methods A facility-based cross-sectional study design was applied from March 1–28, 2021. One hundred and thirty-six health institutions were selected by simple random sampling method. Data was collected using the observation check list and interviewer-administered pre-tested structured questionnaires. Data was analyzed using SPSS version 25. The binary logistic regression was employed and those variables with a p -value less than 0.25 in the bivariate analysis were used for multivariable logistic regression. Then multivariate analysis at a p -value <0.05 and AOR with 95% CI was used to measure the degree of association between independent variables and the outcome variable. Results The study indicates that 83 (61%) public health facilities had good cold chain management practice at 95% CI (52.2–68.4). Experience greater than 2 years (AOR=2.8, 95% CI=1.13–6.74), good knowledge on cold chain management (AOR=3.02, 95% CI=1.2–7.4), training on cold chain management (AOR=1.86, 95% CI=1.36–9.84), and supportive supervision on cold chain management (AOR=2.71, 95% CI=1.1–7.14) were statistically significantly associated with good cold chain management practice. Conclusion The result of the study indicated that there was low cold chain management practice in the study area. Strengthening the knowledge of healthcare workers and supportive supervision on cold chain management by giving training and monitoring their practice toward cold chain management may help to improve the cold chain management practice.