Several studies have focused on umbilical cord-derived mesenchymal stem cells (UC-MSCs) due to their potential therapeutic effects in a cluster of diseases. However, there has been no bibliometric analysis evaluating the evolution in UC-MSC research. Therefore, this study aimed to assess scientific activity regarding UC-MSC research. Publications on UC-MSCs were retrieved from the Science Citation Index-Expanded (SCI-E) of the Web of Science (WoS) from 1975 to 2017. Statistical analyses were performed using Excel, GraphPad Prism 5, and VOSviewer software. Comparative analyses were employed to assess contributions between different countries, institutes, and researchers. With 21.26 citations per paper, 1206 papers cited 25,517 times were included. Mainland China contributed the most with 558 papers, with the most citations (6858 times) and the highest H-index (43). South Korea ranked first for number of papers per million people and per trillion gross domestic product (GDP). Keywords were stratified into two clusters by VOSviewer software: cluster 1, "treatments and effects"; and cluster 2, "characteristics". The average appearing years (AAY) of keywords in cluster 1 was more recent than that in cluster 2. For promising hotspots, "TNF-α" showed the latest AAY at 2014.09, followed by "migration", "angiogenesis", and "apoptosis". We conclude that the number of publications has been continuously growing dramatically since 2002 and that mainland China and South Korea are the most productive regions. The focus gradually shifts from "characteristics" to "treatments and effects". Attention should be drawn to the latest hotspots, such as "TNF-α", "migration", "angiogenesis", and "apoptosis". Furthermore, funding agencies might increase investments in exploring the therapeutic potential of UC-MSCs.