Cord blood is a rich source of hematopoietic stem cells used to treat many diseases of blood origin. Thus, storage banks were created to store and provide umbilical cord cells. With the development of diagnostic and therapeutic technologies and techniques in medicine, ethical issues have also become more widespread and complex. After the creation of the cord blood banks, efforts were made to address the ethical issues associated with such banks. The present study attempts to identify the ethical challenges in these banks in the published studies. Databases including PubMed, Scopus, Web of Science (WOS), Embase, Proquest, and Google Scholar were searched from January 1996 to January 2021. Then, the ethical challenges of the cord blood bank were extracted from the results section using thematic content analysis. 22 studies were selected based on inclusion and exclusion criteria. The ethical challenges raised in the studies included private or public ownership of the bank, fair access to banking services, informed and voluntary consent, failure to provide sufficient information to individuals about the process, confidentiality of user’s information, conflict of interest of bank founders (who are commonly doctors). The findings of this study indicated that there are serious ethical concerns regarding umbilical cord blood banks. Responding clearly to these ethical challenges calls for the attention of policymakers and medical ethics professionals; this will require a clear statement of the various aspects of these banks for society.