Oocyte cytoplasmic maturation is a crucial process during in vitro maturation (IVM), and finding an appropriate IVM medium that promotes oocyte competence is very critical in assisted reproductive technology (ART). The aim of this study was to investigate the effects of umbilical cord Wharton’s jelly (WJ-MSCs)-derived conditioned media on the maturation of immature oocytes and their developmental potential in humans after IVM, as well as apoptotic gene expression. A total of 392 germinal vesicle (GV) oocytes were collected from 207 women aged 25–35 years and divided into two IVM groups: (1) control group, which was cultured in CleavTM medium, and (2) experimental group, which was cultured in supernatants of umbilical cord Wharton’s jelly as a conditioned medium (CM). First, WJ-MSCs were isolated, and their purity was analyzed. The immunophenotypes of WJ-MSCs were analyzed by flow cytometry. The quantitative expression of BCL2, BAX, and BAG1 in matured oocytes and embryos was evaluated through quantitative real-time polymerase chain reaction (qRT-PCR). Our findings showed that WJ-MSCs have a high proliferating capacity. The purity of the isolated cells was further validated by immunophenotyping, which revealed that their surface antigen expression had phenotypical properties similar to WJ-MSCs. When compared to CD34 and CD45 surface markers, the enlarged cells were positive for CD90, CD105, and CD44. There were significant differences in cytoplasmic maturation of oocytes and embryo quality between the two groups. The mRNA expression levels of BCL-2, BAG1, and BAX in matured oocytes and embryos were also significantly different between the two groups. Therefore, WJ-MSCs medium indicated potential efficacy in terms of ameliorating oocyte maturation and in promoting the development and genes expression of BAX, BCL-2, and BAG1.