In this letter, we propose a point cloud structural similarity-based loop detection method for underwater Simultaneous Localization and Mapping using sonar sensors. Existing sonar-based loop detection approaches often rely on 2D projection and keypoint extraction, which can lead to data loss and poor performance in feature-scarce environments. Additionally, methods based on neural networks or Bag-of-Words require extensive preprocessing, such as model training or vocabulary creation, reducing adaptability to new environments. To address these challenges, our method directly utilizes 3D sonar point clouds without projection and computes point-wise structural feature maps based on geometry, normals, and curvature. By leveraging rotation-invariant similarity comparisons, the proposed approach eliminates the need for keypoint detection and ensures robust loop detection across diverse underwater terrains. We validate our method using two real-world datasets: the Antarctica dataset obtained from deep underwater and the Seaward dataset collected from rivers and lakes. Experimental results show that our method achieves the highest loop detection performance compared to existing keypointbased and learning-based approaches while requiring no additional training or preprocessing. Our code is available at https://github.com/donghwijung/point_cloud_structural_similarity_based_underwater_sonar_loop_detection.