Gluten-free products made from naturally gluten-free raw materials have an inferior taste and can cause deficiencies in various nutrients, especially non-starch polysaccharides. To address this problem, scientists are searching for new strategies to eliminate harmful gluten from wheat, rye, and barley and to produce balanced products with good organoleptic properties. This study evaluated the possibility of hydrolysing gluten in wheat bran, a by-product obtained after the dry fractionation of wheat, using plant enzymes. The gluten content of wheat bran after treatment with papain, bromelain, and their combination under different hydrolysis conditions was investigated. The amount of gluten was determined using an enzyme-linked immunosorbent assay ELISA R5 and the reduction in immunogenic gliadins was analysed using high-performance reverse phase liquid chromatography. The results of the study showed that 4 h hydrolysis with bromelain and papain reduced the levels of gluten immunogenic compounds in bran from 58,650.00 to 2588.20−3544.50 mg/kg; however, they did not reach the gluten-free limit. A higher hydrolysis efficiency of 95.59% was observed after treatment with papain, while the combination of both enzymes and bromelain alone were less effective. The results presented in this article will be helpful to other researchers and manufacturers of wheat-based products when selecting methods to reduce gluten immunogenicity and contribute to the development of sustainable technologies.