Category-level object pose and shape estimation from a single depth image has recently drawn research attention due to its wide applications in robotics and self-driving. The task is particularly challenging because the three unknowns, object pose, object shape, and model-to-measurement correspondences, are compounded together but only a single view of depth measurements is provided. The vast majority of the prior work heavily relies on data-driven approaches to obtain solutions to at least one of the unknowns and typically two, running with the risk of failing to generalize to unseen domains. The shape representations used in the prior work also mainly focus on point cloud and signed distance field (SDF). In stark contrast to the prior work, we approach the problem using an iterative estimation method that does not require learning from any pose-annotated data. In addition, we adopt a novel mesh-based object active shape model that has not been explored by the previous literature. Our algorithm, named ShapeICP, has its foundation in the iterative closest point (ICP) algorithm but is equipped with additional features for the category-level pose and shape estimation task. The results show that even without using any pose-annotated data, ShapeICP surpasses many data-driven approaches that rely on the pose data for training, opening up new solution space for researchers to consider.