The food industry has significantly expanded and become globalized due to the growth of the economies of many countries and an increasing world population. The industry is consequently facing major sustainability challenges. Food, which is critical to the existence of humanity and is affected by the world’s ecosystems and human intervention, is a fundamental issue within academic research, especially in terms of sustainability. Using a bibliometric approach, this paper analyzed studies on sustainability in the food industry in the context of the most cited articles, trends in the number of articles, most influential journals, most influential authors, most productive and influential institutions and countries, and future research directions. The software tools Bibliometrix 3.1.4 R-package and VOSviewer 1.6.18.0 were used together to analyze the dataset, which was obtained from the Web of Science database. The results indicated that Sustainability, Journal of Cleaner Production, and Frontiers in Sustainable Food Systems are the most important journals in this field, with the greatest number of articles published. Analyses of the network and overlay visualization of keyword co-occurrences identified six different research clusters. Since climate change and food security issues are in alignment with each other, sustainable food chains and social aspects are an important cross-cutting area of research. The results showed that future research should be multi-disciplinary and involve adjacent fields, including agriculture, agroecology, and climate science. There is also a need for research in the field of economic and social sustainability in the food industry. Studying the research topics found in the thematic map analysis, such as the effect of a sustainable diet on the food chain and the relationships among the agri-food system, sustainable agriculture, sustainable food systems, and sustainability of the food chain, is recommended for future research.