Motion prediction is essential for safe and efficient autonomous driving. However, the inexplicability and uncertainty of complex artificial intelligence models may lead to unpredictable failures of the motion prediction module, which may mislead the system to make unsafe decisions. Therefore, it is necessary to develop methods to guarantee reliable autonomous driving, where failure detection is a potential direction. Uncertainty estimates can be used to quantify the degree of confidence a model has in its predictions and may be valuable for failure detection. We propose a framework of failure detection for motion prediction from the uncertainty perspective, considering both motion uncertainty and model uncertainty, and formulate various uncertainty scores according to different prediction stages. The proposed approach is evaluated based on different motion prediction algorithms, uncertainty estimation methods, uncertainty scores, etc., and the results show that uncertainty is promising for failure detection for motion prediction but should be used with caution.