Deployment of the Micro Aerial Vehicle (MAV) in real-life applications poses multiple challenges, specially when there are external forces such as wind gust or interaction to the environment. Thus, this article proposes a novel Nonlinear Moving Horizon Estimation (NMHE) for estimating the external forces without adding extra sensor to the MAV or using external sensor for force measurements. The proposed method uses only the dynamic model, while avoiding the need to know aerodynamic models or other parameters of the MAV. The NMHE problem is solved using Proximal Averaged Newton-type method for Optimal Control (PANOC), which is a fast numerical optimization, completely matrix-free, not sensitive to ill conditioning, and involves only simple algebraic operations. The solver has the ability to provide the estimation of the states and external forces, such as wind at a rate of 5 ms, which can be used online for the MAV controller. The proposed method is evaluated in a closed loop simulation environment with position controller in present of measurement noise and varying external forces, while it results to the fast convergent of the state and external force estimations.