This paper deals with the distributed fault estimation problem for large-scale interconnected systems subject to intermittent measurements. To take full use of the available measurements and achieve acceptable accuracy, a novel distributed hybrid observer scheme with intersample injection terms is proposed to provide smooth and continuous estimations of the system state and faults. Then, with the help of the hybrid system theory, sufficient conditions are provided to ensure the exponential input-to-state stability of the estimation errors, and the performance of the designed distributed hybrid observer scheme is analyzed detailedly by characterizing the properties of intermittent measurement innovation. Compared with the existing fault estimation observers, the requirements for continuous or periodical communication are removed, and thus the designed observer is more applicable to the embedded communication networks. Finally, a simulation example of two inverted pendulums interconnected as a line by springs is given to further demonstrate the effectiveness of the presented scheme.