The carbon emissions trading market is an essential tool for addressing climate change. The carbon emissions trading market has a relatively short history, and the research and management of risks in this market require further development. This paper takes as its research object 1272 pieces of English literature studies published by international scholars and featured on the Web of Science between 2002 and 2024. It uses CiteSpace software to categorize changes in the trends related to carbon market risk research based on time, space, and keyword clustering mapping. The results reveal the following: (1) In terms of the timeline, the risk evolution of the international carbon market is divided into an embryonic period (2002–2007), a developmental period (2008–2018), and a prosperous period (2019–2024); (2) from the perspective of spatial distribution, carbon market risk research institutions are multipolar, with China, the United States, and the United Kingdom, among other countries, issuing more studies on the topic; these studies mainly emerge from universities and research institutions; and (3) in terms of research hotspots, they revolve around four disciplinary issues, namely, primary research related to carbon market risk, carbon market risk categories, carbon market risk measurement, and response programs.