A segmentation algorithm based on the geometric features of a point cloud is proposed to solve the difficulty of detecting defects such as small weld puddles and weld tumors generated in the laser welding process of power battery covers. First, the point-cloud data acquired by the defect detection platform is filtered and denoised. Second, numerous non-weld-region point clouds are eliminated via the established weld coarse segmentation model, and the curvature threshold adaptive algorithm is used to achieve the accurate segmentation of weld seams. Subsequently, the region growth algorithm is improved by introducing Euclidean distance feature data to achieve the accurate segmentation of defects in the weld seams. Finally, the geometric dimensions of the extracted defects are calculated based on the measured model. The experimental results show that the average measurement error obtained by the proposed method is 0.041 mm, and the average measurement accuracy is improved by 77%, which meets the detection requirements and is of great significance for the intelligent detection of laser welding defects.