A reactive three-dimensional maneuver strategy for a multirotor Unmanned Aerial Vehicle (UAV) is proposed based on the collision cone approach to avoid potential collision with a single moving obstacle detected by an onboard sensor. A Light Detection And Ranging (LiDAR) system is assumed to be mounted on a hexacopter to obtain the obstacle information from the collected point clouds. The collision cone approach is enhanced to appropriately deal with the moving obstacle with the help of a Kalman filter. The filter estimates the position, velocity, and acceleration of the obstacle by using the LiDAR data as the associated measurement. The obstacle state estimate is utilized to predict the future trajectories of the moving obstacle. The collision detection and obstacle avoidance maneuver decisions are made considering the predicted trajectory of the obstacle. Numerical simulations, including a Monte Carlo campaign, are conducted to verify the performance of the proposed collision avoidance algorithm.