The effective fault detection of wind turbines (WTs) can greatly help to improve their availability and reduce their operation and maintenance costs. In this context, data-driven fault detection approaches have attracted a lot of interests due to the availability of a large amount of monitoring sensor data containing rich information related to health conditions of WTs. However, sensor data collected from WTs are naturally multivariate and highly nonlinear correlated with redundant information and significantly contaminated measurement noise, which makes the WT fault detection more challenging. To this end, this paper develops a multivariate data-driven fault detection (MDFD) framework based on a recently emerged neural network algorithm named denoising autoencoder (DAE). Instead of using a single fixed noise level in the traditional DAE, a novel multi-level-denoising autoencoder (MLD-AE) method is proposed to enhance the representation learning ability by designing different multi-level noise adding schemes. The proposed MLD-AE could better discover useful patterns at multiple corrupted scales and capture nonlinear dependencies from noisy multivariate sensor data, therefore robustly reconstruct the original signal with the preserved largest information. The proposed framework and method are evaluated on both simulated data from a generic 5 MW WT benchmark and SCADA data from a real wind farm. The results demonstrate that our proposed MLD-AE-based fault detection approach significantly outperforms traditional DAE, AE, and linear PCA approaches, which has great potentials for practical applications in the wind industry.