Vaccine hesitancy remains a serious global threat to achieve herd immunity, and this study aimed to assess the magnitude and associated factors of coronavirus disease-19 (COVID-19) vaccine hesitancy among healthcare workers (HCWs) in Amhara regional referral hospitals. A web-based anonymised survey was conducted among 440 HCWs in the Amhara region referral hospitals. The questionnaire was designed using Google Forms and distributed using telegram and e-mail from 15 May to 10 June 2021 to the randomly selected participants in each hospital. The data were analysed with Stata 14.0 and described using frequency tables. A multivariable binary logistic regression model was fitted and model fitness was checked with the Hosmer-Lemeshow goodness of fit test. Out of 440 participants, 418 were willing to participate in the study and the mean age was about 30 years. Overall, 45.9% (n = 192) of participants reported vaccine hesitancy. After applying multivariate analysis, age ≤25 years (adjusted odds ratio (aOR) = 5.6); do not wear a mask (aOR = 2.4); not compliance with physical distancing (aOR = 3.6); unclear information by public health authorities (aOR = 2.5); low risk of getting COVID-19 infection (aOR = 2.8); and not sure about the tolerability of the vaccine (aOR = 3.76) were associated with COVID-19 vaccine hesitancy. A considerable proportion of HCWs were hesitant towards COVID-19 vaccine, and this can be tackled with the provision of clear information about the vaccine.