The potential use of onboard vision sensors (e.g., cameras) has long been recognized for the Sense and Avoid (SAA) of unmanned aerial vehicles (UAVs), especially for micro UAVs with limited payload capacity. However, vision-based SAA for UAVs is extremely challenging because vision sensors usually have limitations on accurate distance information measuring. In this paper, we propose a monocular vision-based UAV SAA approach. Within the approach, the host UAV can accurately and efficiently avoid a noncooperative intruder only through angle measurements and perform maneuvers for optimal tradeoff among target motion estimation, intruder avoidance, and trajectory tracking. We realize this feature by explicitly integrating a target tracking filter into a nonlinear model predictive controller. The effectiveness of the proposed approach is verified through extensive simulations.