Soy beverages (SB) are the most popular beverage in the expanding market of plant-based drinks. They provide high-quality protein and polyphenols and are often Ca-fortified as a milk alternative. This work evaluated the antioxidant potential, the mineral content, and the fatty acid profiles found in SB, analysing as well the bioaccessibility of some nutrients after INFOGEST static digestion. Five types of SB available in the market, including Ca-fortified, high-protein, and low-fat drinks, were analysed. Ca supplementation and high protein content in the beverages significantly enhanced Ca bioaccessibility. The lipid profile demonstrated substantial changes during digestion, due to drastic reductions in saturated fatty acids and marked increases in polyunsaturated fatty acids in the bioaccessible fractions; these changes were mainly related to the content levels of Ca and polyphenols in the beverages. Significant increases in the antioxidant properties, as measured by ABTS and FRAP assays, were noticed after the digestive process. Additionally, ROS generation in Caco-2 cells after induced oxidative damage was prevented by the BF of digested SB. The digested low-fat drink, which also had a low level of protein content, showed the least antioxidant activity. In conclusion, composition of the soy drink considerably affected the bioaccessibility of nutritional components and the drink’s antioxidant potential.