Monascus red pigments (MRPs) are mainly used as natural food colorants; however, their application is limited due to their poor stability. To expand their areas of application, we investigated the binding constants and capacity of MRPs to whey protein isolate (WPI) and whey protein hydrolysate (WPH) and calculated the surface hydrophobicities of WPI and WPH. MRPs were combined with WPI and WPH at a hydrolysis degree (DH) of 0.5% to form the complexes (DH = 0.0%) and (DH = 0.5%), respectively. Subsequently, the structural characteristics of complex (DH = 0.5%) and WPI were characterized and the color retention rates of both complexes and MRPs were investigated under different pretreatment conditions. The results showed that the maximum binding constant of WPI with MRPs was 0.670 ± 0.06 U−1 and the maximum binding capacity was 180 U/g. Furthermore, the thermal degradation of complex (DH = 0.0%), complex (DH = 0.5%), and MRPs in a water bath at 50–100 °C followed a first-order kinetic model. Thus, the interaction of WPI with MRPs could alter the protein conformation of WPI and effectively protect the stability of MRPs.