Traditional high-quality 3D scanning and reconstruction typically relies on human labor to plan the scanning procedure. With the rapid development of embodied systems such as drones and robots, there is a growing demand of performing accurate 3D scanning and reconstruction in an fully automated manner. We introduce Auto3R, a data-driven uncertainty quantification model that is designed to automate the 3D scanning and reconstruction of scenes and objects, including objects with non-lambertian and specular materials. Specifically, in a process of iterative 3D reconstruction and scanning, Auto3R can make efficient and accurate prediction of uncertainty distribution over potential scanning viewpoints, without knowing the ground truth geometry and appearance. Through extensive experiments, Auto3R achieves superior performance that outperforms the state-of-the-art methods by a large margin. We also deploy Auto3R on a robot arm equipped with a camera and demonstrate that Auto3R can be used to effectively digitize real-world 3D objects and delivers ready-to-use and photorealistic digital assets. Our homepage: https://tomatoma00.github.io/auto3r.github.io .