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Motion planners are essential for the safe operation of automated vehicles across various scenarios. However, no motion planning algorithm has achieved perfection in the literature, and improving its performance is often time-consuming and labor-intensive. To tackle the aforementioned issues, we present DrPlanner, the first framework designed to automatically diagnose and repair motion planners using large language models. Initially, we generate a structured description of the planner and its planned trajectories from both natural and programming languages. Leveraging the profound capabilities of large language models in addressing reasoning challenges, our framework returns repaired planners with detailed diagnostic descriptions. Furthermore, the framework advances iteratively with continuous feedback from the evaluation of the repaired outcomes. Our approach is validated using search-based motion planners; experimental results highlight the need of demonstrations in the prompt and the ability of our framework in identifying and rectifying elusive issues effectively.