This article investigates the fault estimation (FE) problem for a class of nonlinear systems via an adaptive fuzzy approach. Considering the limited communication capacity of networks, the quantized measurement signals are used to construct adaptive laws instead of the real measurements in the designed fuzzy observer. By injecting the quantizer parameter into the observer inputs, the quantization effects on the convergence of estimation errors can be compensated. It is also shown that nondifferentiable actuator faults can be reconstructed by the developed FE approach. Finally, two simulation examples are provided to illustrate the validity of the presented scheme.