In this work, wheat bread was fortified with fibre enriched extracts recovered from agroindustry by-products, namely, elderberry skin, pulp and seeds (EE); orange peel (OE); pomegranate peel and interior membranes (PE); and spent yeast (YE). The impact of this fortification on the total and bioaccessible mineral composition of wheat breads, estimated mineral daily intake, and the relationship between bioaccessibility and dietary fibre was evaluated. Fortification with OE, EE, and PE improved the content of essential minerals in bread when compared to control bread. The exception was bread fortified with YE, which presented a mineral content similar to control bread, but its mineral bioaccessibility was significantly higher than in all the other bread formulations. The opposite was observed for PE bread, which presented a significant reduction of bioaccessible minerals. We concluded that the origin of the fibre rich extract must be carefully selected, to avoid potential negative impact on mineral bioaccessibility.