This paper presents a new approach based on ant colony optimization (ACO) to determine the trajectories of a fleet of unmanned air vehicles (UAVs) looking for a lost target in the minimum possible time. ACO is especially suitable for the complexity and probabilistic nature of the minimum time search (MTS) problem, where a balance between the computational requirements and the quality of solutions is needed. The presented approach includes a new MTS heuristic that exploits the probability and spatial properties of the problem, allowing our ant based algorithm to quickly obtain high-quality high-level straight-segmented UAV trajectories. The potential of the algorithm is tested for different ACO parameterizations, over several search scenarios with different characteristics such as number of UAVs, or target dynamics and location distributions. The statistical comparison against other techniques previously used for MTS (ad hoc heuristics, cross entropy optimization, bayesian optimization algorithm and genetic algorithms) shows that the new approach outperforms the others.