In this study, the problem of fuzzy hybrid observer-based fault estimation design is systematically investigated for Eular-Lagrange systems with aperiodic measurements. By exploiting the hybrid system theory and the fuzzy logic technique, a novel fuzzy hybrid observer scheme is proposed to achieve the purpose of fault estimation. Specifically, an intersample injection term is introduced, which plays the role of output error correction term when the output measurements are unavailable and is updated together with the state variables of the designed observer when new measurements arrive. In addition, the estimation error system is incorporated with a timer variable triggering the arrival of a new measurement and the observed performance is discussed within the hybrid systems framework, which is helpful to fully reveal the property of the intermittent measurement transmissions and construct sufficient conditions for guaranteeing the convergence of the estimation errors. Finally, the performance and effectiveness of the proposed hybrid observer scheme are illustrated with a simulation example.