Electronic retailing (e-retail) is a type of retailing where the retailer and customers communicate via web and mobile applications. In order for e-retail businesses to continue to grow in an increasingly competitive environment and to stand out from competing businesses, they need to be able to respond to changing consumer demands in a timely and accurate manner. A demand forecasting study using Machine Learning and Deep Learning algorithms for the e-retail sector with local supermarkets' data in Turkey (as far as we know) has not been carried out yet. In this study, the demand for a certain category of products was estimated by considering the two-year e-commerce data (website and mobile application) of a local supermarket for the years 2019-2020 and the factors affecting product sales (holidays, CPI value and unemployment rate). Twenty-four different methods of six different artificial intelligence algorithms (Deep Learning, Artificial Neural Networks, Gaussian Process Regression, Regression Tree, Support Vector Regression and Ensemble Learning) were used to obtain the best demand forecasting model. The obtained results were evaluated using correlation coefficient (R), Root Mean Square Error (RMSE), and Mean Absolute Error (MAE) criteria. The best result was obtained using Long Short-Term Memory Networks (RMSE= 0.0353; MAE= 0.0164; R = 0.9742). The results obtained will be able to increase the success of e-retail sales by using the product supply in the right quantities, in sales campaigns, and in marketing strategies.