The inherent time-varying nature of the wind farm power causes undesired voltage flicker in the power network. In order to mitigate the flicker to enhance the performance of the wind power system with very fast dynamics, the static VAr compensator (SVC) is utilized. However, the SVC operates with some delays which negatively affects its performance. This persuades us to predict the reactive power of the wind farm to compensate for the real-world delay. The predicted reactive power is then utilized in the SVC. Therefore, this paper develops a novel fuzzy one-step-ahead prediction approach for the wind farm reactive power. The proposed fuzzy prediction uses a Takagi-Sugeno (TS) fuzzy representation whose unknown parameters are tuned online based on an extended Kalman filter (EKF). The wind farm is modeled as a time-varying current source which its amplitude and phase change every 0.01 s. A large set of the actual data of a wind farm in Manjil, Iran is gathered and directly utilized in the simulation process. Several flicker indices are calculated to evaluate the proposed prediction method. The obtained results show the performance enhancement and flicker mitigation of the suggested power scheme.