Irritable bowel syndrome (IBS) is a functional disorder of the gastrointestinal system. Adherence to a low-FODMAP (fermenting oligosaccharides, disaccharides, monosaccharides, and polyols) diet may be one of the solutions in this case. The major FODMAP carbohydrates found in wheat bread are fructans. The objective of this study was to produce wheat bread with a reduced fructans content. Breads were made from light and whole grain flour obtained from common wheat using two methods of dough development—I-stage method with the use of yeast, and II-stage method with the use of yeast and sourdough with a pure culture of Lactobacillus plantarum. Four different fermentation times were tested—60, 90, 120, and 150 min. Afterwards, quality attributes (loaf volume, crust and crumb color, and sensory properties) of the produced breads were evaluated, and the fructans content was determined. The results demonstrated that all the factors influenced the quality of wheat breads, as well as their fructans content. Breads made with the II-stage method and light flour had a lower content of fructans, which was decreased in breads along with extending the time of dough fermentation. The greatest impact on fructans content decrease in wheat bread was ascribed to the use of light flour, the II-stage method of dough development coupled with a dough fermentation time prolongation to 150 min.