We investigate the problem of distributed sensors' failure detection in networks with a small number of defective sensors, whose measurements differ significantly from neighbouring sensor measurements. We build on the sparse nature of the binary sensor failure signals and propose a new distributed detection algorithm based on Group Testing. The distributed GT algorithm estimates the set of defective sensors by a low complexity distance decoder from a small number of linearly independent binary messages exchanged by the sensors. We first consider networks with one defective sensor and determine the minimal number of linearly independent messages needed for detection of the defective sensor with high probability. We then extend our study to the detection of multiple defective sensors by modifying appropriately the message exchange protocol and the decoding procedure. We show through experimentation that, for small and medium sized networks, the number of messages required for successful detection is actually smaller than the minimal number computed in the analysis. Finally, simulations demonstrate that the proposed method outperforms methods based on random walks in terms of detection performance and convergence rate.