This paper describes an obstacle avoidance system for low-cost Unmanned Aerial Vehicles (UAVs) using vision as the principal source of information through the monocular onboard camera. For detecting obstacles, the proposed system compares the image obtained in real time from the UAV with a database of obstacles that must be avoided. In our proposal, we include the feature point detector Speeded Up Robust Features (SURF) for fast obstacle detection and a control law to avoid them. Furthermore, our research includes a path recovery algorithm. Our method is attractive for compact MAVs in which other sensors will not be implemented. The system was tested in real time on a Micro Aerial Vehicle (MAV), to detect and avoid obstacles in an unknown controlled environment; we compared our approach with related works.