The World Health Organisation (WHO) recommends that all babies be exclusively breastfed, stating that donor milk is the next best alternative in the absence of the mother’s own milk. Milk sharing takes many forms, namely wet nursing, co-feeding, cross-feeding, and a human milk bank (HMB). However, the establishment of a human milk bank is still not widely accepted and is a debatable topic because of religious concerns in Malaysia. The aim of this study is to determine the facilitators and barriers among Malaysians towards the acceptance of an HMB. A cross-sectional study with 367 participants was conducted; the participants answered an online-validated, self-administered questionnaire. Data on sociodemographic, knowledge on breastfeeding benefits, knowledge and attitude on HMB-specific issues were analysed in terms of frequency before proceeded with multiple logistic regression. The majority of the respondents were Muslim (73.3%), had completed their tertiary education (82.8%), and were employed (70.8%). Only 55.9% of respondents had heard of HMB, stating the internet as their main source of information, but many respondents were agreeable to its establishment (67.8%). Most respondents had a good score on knowledge of breastfeeding benefits and on HMB-specific issues (70% and 54.2%, respectively), while 63.8% had a positive attitude towards HMB. In the multivariate analysis, mothers with a good score on general knowledge of breastfeeding (AOR: 1.715; 95% CI 1.047–2.808) were more likely to accept the establishment of HMB, while being a Muslim was negatively associated with its establishment (AOR = 0.113, 95% CI 0.050–0.253). The study found a high prevalence of mothers who were willing to accept the establishment of HMB. By educating mothers on the benefits of breastfeeding, as well as addressing their religious concerns, the establishment of a religiously abiding HMB in Malaysia may be accepted without compromising their beliefs or the health benefit of donor milk.