The effect of sodium alginate on the denaturation and aggregation behavior of bovine serum albumin and hen egg-white lysozyme was studied. Large amounts of polysaccharide increase the thermal stability of albumin due to the weak binding interactions. At the same time, sodium alginate can reduce the quantity of amyloid fibrils formed by albumin under denaturing conditions, which is a consequence of the stabilization of the native protein form by glycan binding. In the case of lysozyme, the polysaccharide has no influence on the thermal stability of the protein in 2 M guanidinium hydrochloride. However, the inhibition of fibril formation with an increase in the lag time was observed, which is explained by the binding of sodium alginate to lysozyme fibrils, but not to the protein monomer. The molecular nature of the binding interactions between alginate and the studied proteins was elucidated using molecular docking and known experimental structures of glycan–protein complexes.