Abstract Background The World Health Organization (WHO) recommends that donor human milk is superior to artificial infant formula in situations where the baby cannot feed on the mother’s breastmilk. The purpose of this study was to determine the acceptability of donor human milk banking among health workers in Zimbabwean urban settings. Methods A cross sectional study was conducted among 535 health workers and 15 key informants. Three referral hospitals were purposively selected and systematic random sampling was used to select the health workers. The study was conducted between October 2017 and October 2018. Results The concept of donor human milk banking was acceptable among health workers. One-third (31%) of the study participants reported that they would accept donor breastmilk for their children while 56% of them would encourage their clients to donate breastmilk. Acceptance of donor human milk banking was associated with a high level of knowledge on breastmilk banks (p = 0.009) and the study participants’ health profession (p = 0.001). Clinical staff were more receptive to donor human milk banking compared to non-clinical health workers. Donor human milk banking was not associated with religion (p = 0.498) or marital status (p = 0.714). Conclusions The results showed that health workers and policy informers would accept the establishment of breastmilk banks subject to resource availability. Commitment to the establishment of breastmilk banks was moderately acceptable among opinion leaders responsible for spearheading health and nutrition policies.