LiDAR odometry is essential for many robotics applications, including 3D mapping, navigation, and simultaneous localization and mapping. LiDAR odometry systems are usually based on some form of point cloud registration to compute the ego-motion of a mobile robot. Yet, few of today's LiDAR odometry systems consider the domain-specific knowledge and the kinematic model of the mobile platform during the point cloud alignment. In this paper, we present Kinematic-ICP, a LiDAR odometry system that focuses on wheeled mobile robots equipped with a 3D LiDAR and moving on a planar surface, which is a common assumption for warehouses, offices, hospitals, etc. Our approach introduces kinematic constraints within the optimization of a traditional point-to-point iterative closest point scheme. In this way, the resulting motion follows the kinematic constraints of the platform, effectively exploiting the robot's wheel odometry and the 3D LiDAR observations. We dynamically adjust the influence of LiDAR measurements and wheel odometry in our optimization scheme, allowing the system to handle degenerate scenarios such as feature-poor corridors. We evaluate our approach on robots operating in large-scale warehouse environments, but also outdoors. The experiments show that our approach achieves top performances and is more accurate than wheel odometry and common LiDAR odometry systems. Kinematic-ICP has been recently deployed in the Dexory fleet of robots operating in warehouses worldwide at their customers' sites, showing that our method can run in the real world alongside a complete navigation stack.