Given that global amounts of waste are growing rapidly, it is extremely important to determine what amount of waste will be generated in the near future. Accurate waste forecasting is also important for planning and designing a sustainable municipal solid waste (MSW) management system. For that reason, there is a need to build a model to predict the amount of MSW generated in the near future. Based on previous research, artificial neural networks (ANN) show better results in predicting waste generation compared to other mathematical models. In this research, an ANN model using the iterative algorithm Broyden–Fletcher–Goldfarb–Shanno (BFGS) for the prediction of MSW fractions, based on the socio-demographic characteristics, economic and industrial data obtained in Croatia and summarized data of the member states of EU (EU-27 from 2020), showed good predictive capabilities. The coefficient of determination during the training cycle for the output variables; household and similar waste (HHS), paper and cardboard waste (PCW), wood waste (WW), textile waste (TW), plastic waste (PW) and glass waste (GW) were 0.993; 0.997; 0.999; 0.997; 0.998; and 0.998, respectively, while reduced chi-square, mean bias error, root mean square error, mean percentage error, average absolute relative deviation and sum of squared errors were found low. In this paper, Yoon′s method of interpretation shows the relationships between socio-demographic data and the amount of generated waste. The results indicate that the lowest level of education shows a negative impact on observed waste-types calculations, with a relative impact between −9.889 and −4.467%. The most pronounced positive impact on the calculation of HHS, PCW, WW, TW, PW and GW was observed for year variable, gross domestic product, exports of goods and services, imports of goods and services, wages and salaries, secondary income, arrivals in collective accommodation establishments, overnight stays in collective accommodation establishments and exports of petroleum and petroleum products to partner countries, with a relative influence of 4.063–7.028; 2828–4851; 5240–6197; 5.308–6.341; 4290–4810; 4533–5805; and 4.345–4.493, respectively. The obtained results indicate that the amount of HHS waste at the EU-27 level in 2025 will decrease by approximately 18% compared to the data from 2018. The quantities of other observed recyclable types of waste will increase by 34% for PCW, 310% for WW, 40% for TW, 276% for PW and about 67% for GW. The amount of waste generated provides the basic information needed to plan, operate and optimize the waste management system. It could also help in the transition to an environmentally friendly and economically profitable circular economy. The model created in this research could also help with the system of separate waste collection, which would lead to more efficient recycling and the achievement of the set goals for recycling 55% of municipal waste by 2025.