In city-wide weather prediction, wind gust information can be obtained using unmanned aerial vehicles (UAVs). Although wind sensors are available, an algorithm-based active estimation can be helpful not only as a weightless substitute but also as feedback for robust control. This paper aims to estimate the wind gusts affecting the quadrotors (a type of UAV) as the input disturbances by using a frequency-based nonlinear disturbance observer (NDOB). To obtain highly accurate estimations, frequency is considered as the main design parameter, thereby focusing the estimation on the frequency range of the wind gusts. The NDOB is developed using the Takagi-Sugeno (T-S) fuzzy framework. In this approach, the twelfth-order nonlinear model is approximated into a sixth-order T-S fuzzy model to reduce computational cost. A two-step verification method is presented, which includes MATLAB/Simulink simulations and the experiments performed using a 2.5 kg quadrotor.