A novel approach for achieving fast evasion in self-localized swarms of unmanned aerial vehicles (UAVs) threatened by an intruding moving object is presented in this paper. Motivated by natural self-organizing systems, the presented approach of fast and collective evasion enables the UAV swarm to avoid dynamic objects (interferers) that are actively approaching the group. The main objective of the proposed technique is the fast and safe escape of the swarm from an interferer discovered in proximity. This method is inspired by the collective behavior of groups of certain animals, such as schools of fish or flocks of birds. These animals use the limited information of their sensing organs and decentralized control to achieve reliable and effective group motion. The system presented in this paper is intended to execute the safe coordination of UAV swarms with a large number of agents. Similar to natural swarms, this system propagates a fast shock of information about detected interferers throughout the group to achieve dynamic and collective evasion. The proposed system is fully decentralized using only onboard sensors to mutually localize swarm agents and interferers, similar to how animals accomplish this behavior. As a result, the communication structure between swarm agents is not overwhelmed by information about the state (position and velocity) of each individual and it is reliable to communication dropouts. The proposed system and theory were numerically evaluated and verified in real-world experiments.