In this paper, we focus on the event-triggered robust state estimation problems for nonlinear networked systems with constant measurement delays against denial-of-service (DoS) attacks. The computation of the extended Kalman filter (EKF) generates errors of linearization approximations, which can result in increased state estimation errors, and subsequently amplifies the linearization errors. DoS attacks interfere with the transmission of measurements sent to the remote robust state estimator by overloading the communication networks, while the communication rate of the communication channel is constrained. Therefore, an event-triggered robust state estimation algorithm based on sensitivity penalization with an explicit packet arrival parameter is derived to defend against DoS attacks and linearization errors. Meanwhile, the presence of measurement delays precludes the direct use of conventional state estimation algorithms, prompting us to devise an innovative state augmentation method. The results of the numerical simulations show that the proposed robust state estimator can appreciably improve the accuracy of state estimation.