Manufacturing companies face significant challenges due to rapid changes in globalized markets and open economies, which are experiencing mega-trends such as urbanization, globalization, and individualization. For sustainable growth, advanced technology is necessary. However, selecting technology is a difficult task due to the wide variety of options in the market. Technology has become a fundamental strategic factor for the growth and profitability of companies. The main objective of this paper is to propose a model and a methodological proposal for technology selection in the context of Industry 4.0 manufacturing. The proposed methodology is divided into three stages: The first stage is of knowledge and intervention, which allows for the socialization of the model and data collection. The second stage is the operational stage, where a hybrid method of FAHP and FANP is used to determine the weights of the factors considered. Lastly, the third stage is the analysis and evaluation stage, where the analysis, discussion, and evaluation of the results take place. To validate the proposed model, the methodology was applied to two case studies in Chilean industrial companies. The results obtained through the FAHP and FANP algorithms enabled decision makers to manage and select the most suitable technology from the wide variety of options available in today’s markets.