The World Health Organization has identified nervous system diseases as one of the biggest public health problems, including autism spectrum disorder (ASD). Considering the extensive benefits of physical activity (PA), the literature on the PA research of ASD has increased each year, but there is a lack of bibliometric analyses in this field. To investigate the research achievements worldwide, this paper adopts bibliometrics to analyze the trend in the academic literature on the PA research of ASD published from 1980 to 2021. The documents were retrieved from the Web of Science database, and the search strategy was to combine the keywords related to “physical activity” and “autism spectrum disorder” by using the Boolean operator tools “OR” and “AND” in the title. A total of 359 English documents were retrieved. Microsoft Excel, Data Wrapper, VOSviewer, and Biblioshiny were used for the visual analysis. We found that the number of published documents increased the fastest from 2017 to 2021, which may be due to the promulgation of the Global Action Plan for Physical Activity 2018–2030 and the influence of COVID-19 on the world. The United States and the University of California systems are in the leading position in this field. Cooperation among countries with different levels of development will help to jointly promote the PA research progress on ASD. The focus themes include “individual effect”, “social support” and “activity dose”. The analysis of the frontier topic points out that researchers are paying increasing attention to how to improve the health and physical fitness of this group through PA. This research clearly puts forward a comprehensive overview, theme focus, and future trends in this field, which may be helpful to guide future research.