In this work, we address a planar non-prehensile sorting task. Here, a robot needs to push many densely packed objects belonging to different classes into a configuration where these classes are clearly separated from each other. To achieve this, we propose employing Monte Carlo tree search equipped with a task-specific heuristic function. We evaluate the algorithm on various simulated and real-world sorting tasks and observe that the algorithm is capable of reliably sorting large numbers of convex and non-convex objects, as well as convex objects in the presence of immovable obstacles.