Prey-predator interactions have received significant attention from research scholars for shaping ecological dynamics. Predator populations balance the ecological system in a natural way by controlling the prey’s high growth rate. But, if the predator population is infected, then what effect the predator has on the system is a very important topic to study. Therefore, in this article, we propose a delay-included predator-prey mathematical model with Monod-Haldane and Holling type-II functional response, where susceptible and infected predators represent two sub-classes of predator species due to disease. It is also believed that some time is required in the incubation process so that the disease can spread from the infected to the susceptible predator. We establish the well-posedness of the system and discuss the existence of feasible equilibrium points with their local stability analysis. The study says that the stable behavior of the system is not affected by the incubation delay. However, the system that exhibits oscillatory behavior in the absence of delay becomes stable in the presence of delay. Disease-spreading delay is responsible for the appearance of multi-time switching dynamics. A high prey growth rate increases the predator population, which causes the system to become destabilized. Although a large value of the half saturation constant has a stabilizing effect, the predator population declines while the prey population inclines. The increasing rate of disease transmission in the predator population suppresses the predator density.