In this article, a distributed fault estimation (DFE) approach for switched interconnected nonlinear systems (SINSs) with time delays and external disturbances is proposed using a novel segmented iterative learning scheme (SILS). First, through the utilization of interrelated information among subsystems, a distributed iterative learning observer is developed to enhance the accuracy of fault estimation results, which can realize the fault estimation of all subsystems under time delays and external disturbances. Simultaneously, to facilitate rapid fault information tracking and significantly reduce sensitivity to interference, a new SILS-based fault estimation law is constructed by combining the idea of segmented design with the method of variable gain. Then, an assessment of the convergence of the established fault estimation methodology is conducted, and the configurations of observer gain matrices and iterative learning gain matrices are duly accomplished. Finally, simulation results are showcased to demonstrate the superiority and feasibility of the developed fault estimation approach.