In high-precision assembly tasks, robotic arms need to avoid static obstacles. However, existing obstacle avoidance methods often interrupt the image-based visual servoing (IBVS) process, which affects task continuity and may induce motion oscillations, thereby reducing positioning accuracy. To address this issue, a real-time visual servoing obstacle avoidance method based on dynamic feature point remapping is proposed. This method constructed a multi-objective optimization model with field-of-view constraints using the geometric parameters of the smallest extensible cuboid of obstacles to solve an optimal avoidance path. Subsequently, the direction vector of the obstacle avoidance path was mapped into the image space, where guiding feature points were dynamically generated from real-time feature points to drive the IBVS controller to achieve obstacle avoidance. To improve motion smoothness, a path smoothing transition mechanism based on the Sigmoid function was designed, and an obstacle avoidance distance-driven adaptive gain function was introduced to dynamically optimize the system convergence rate. Finally, the global stability of the closed-loop system was proven through Lyapunov stability analysis. The axle-hole positioning experiments demonstrated that, under different initial poses, the method could generate feasible obstacle avoidance paths in real time, while the motion trajectories of the robotic arm end-effector and the feature points remained smooth without abrupt changes, achieving fast and high-precision convergence with an uninterrupted IBVS process throughout the task. The proposed method realizes a unified closed-loop integration of obstacle avoidance planning and IBVS control, which can provide a practical solution for real-time obstacle avoidance of robotic arms in high-precision assembly tasks requiring safety, continuity and accuracy.