A biotechnology process that employs membrane technology for obtaining an extract rich in tannins of ellagic acid from blackberries (Rubus spp.) and from other fruits that contain these compounds, as well as to the extract obtained using this method. The method is essentially based on baromembrane technologies that allow mechanical separation and effective fractionation between the polyphenol compounds, by interactions between the physico-chemical properties thereof, the material of the membrane and the molar mass of same, thereby allowing enrichment of a fraction of the natural extract with ellagic acid tannins and modification of the content thereof in terms of anthocyanins and other compounds such as sugars and acids.