The study aimed to develop a biorefining process to recover proteins and dietary fibres from a food industry sidestream, canola (Brassica napus) oil pressing residues. The materials were treated with commercial protease, carbohydrase, and phytase to obtain protein-rich supernatants and fibre-rich precipitates. The compositions of these fractions were analyzed using LC-MS (glucosinolates and phenolics) and GC–MS (sugars, acids, and amino acids). Compared to raw material, the supernatants were richer in proteins, sugars, acids, amino acids, phenolic acids, and flavonols; the precipitates had higher levels of minerals and dietary fibres. The enzymatic treatment decreased the contents of phytic acid, glucosinolates, and phenolic alkaloids in all fractions. The applied enzymes effectively enhanced solubility of proteins, despite the lower yield of crude proteins compared to the alkaline extraction (40–82 vs 91 g/100 g dry matters). The impact of enzymes on other chemical components was also revealed by using principal component analysis.