The COVID-19 pandemic has wreaked havoc in every country in the world, with serious health-related, economic, and social consequences. Since its outbreak in March 2020, many researchers from different fields have joined forces to provide a wide range of solutions, and the support for this work from artificial intelligence (AI) and other emerging concepts linked to intelligent data analysis has been decisive. The enormous amount of research and the high number of publications during this period makes it difficult to obtain an overall view of the different applications of AI to the management of COVID-19 and an understanding of how research in this field has been evolving. Therefore, in this paper, we carry out a scientometric analysis of this area supported by text mining, including a review of 18,955 publications related to AI and COVID-19 from the Scopus database from March 2020 to June 2021 inclusive. For this purpose, we used VOSviewer software, which was developed by researchers at Leiden University in the Netherlands. This allowed us to examine the exponential growth in research on this issue and its distribution by country, and to highlight the clear hegemony of the United States (USA) and China in this respect. We used an automatic process to extract topics of research interest and observed that the most important current lines of research focused on patient-based solutions. We also identified the most relevant journals in terms of the COVID-19 pandemic, demonstrated the growing value of open-access publication, and highlighted the most influential authors by means of an analysis of citations and co-citations. This study provides an overview of the current status of research on the application of AI to the pandemic.