The food security of the European Union heavily relies on the food quality systems where Geographical Indications (GI) play an important role. European food is considered world-wide secure and high quality, therefore European food names and designations represent value that should be protected as intellectual property. Despite the importance of GIs in Europe, the availability of the related economic data is very limited, and the only available comprehensive database (in the case of GI foods, the Database of Origin and Registration (DOOR)) details only some very basic and mainly administrative characteristics of such products. From an economic perspective, market size and price premium of these products are the most important in order to assess the economic sustainability of European GI foods. Empirical datasets describing these characteristics of GI products are scarcely available and can be collected only case by case. Therefore, the purpose of this study is to estimate the market size for food products with geographical indications available in Hungary (excluding wines and spirits) and their price premium compared to their direct substitute products, based on empirical data. We conducted monthly mystery shopping for one year (January–December 2018) at three food discount stores (Lidl, Aldi, and Penny Market) operating in Budapest. We collected data on all the GI products available in the stores and their closest substitutes; then the dataset was subsequently analysed and compared to the main characteristics of the DOOR database. The reason for choosing the discounters is that these stores have expanded spectacularly in recent years and are mostly available to average consumers, both in Hungary and across Europe, and based on the main characteristics of this type of retail (limited product portfolio targeting price-sensitive consumers), the data collected here can be considered to indicate the minimum level of market share and price premium. Our results show that currently, GIs have only limited importance in the Hungarian food market, in terms of both the number of products and their market share, as only a small number of such products appear in the food discounters’ supply. As regards the premium achievable with consumer prices, the average price premium is remarkably high (43% on average), even in the case of discounters. Our empirical results also suggest that in Hungary, there is an opportunity to increase the importance of GI foods, both in terms of availability and market share. For Hungarian GI food producers and processors, the level of price premium achievable in discounters might be attractive enough to stimulate their presence in the market.