Milk protein concentrate (MPC) is a high-protein dairy product. It is underutilized due to its poor solubility compared with other milk protein products. This study aimed to investigate the effect of enzymatic hydrolysis on the physicochemical properties and solubility of MPC. Results showed that Alcalase hydrolysates possessed a higher degree of hydrolysis (DH) than Protamex and Flavourzyme hydrolysates. Similar results could be obtained using sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE). The molecular weight of the hydrolysate of Alcalase was less than 10 kDa. Changes to the molecular weight thereby led to a modification in the fluorescence intensity, Fourier-transform infrared spectrometry, and ultraviolet absorption. The solubility of all hydrolysates was significantly increased (p < 0.05). Correlation analysis showed a positive correlation between solubility, DH, and bitterness; the correlation coefficients were 0.81 for DH and 0.61 for bitterness. Electronic tongue analysis showed that the bitterness of Alcalase hydrolysates was the highest, while the values for Protamex hydrolysates were the lowest.