Air bearing-guided linear motion modules have so little friction that they are widely used for precision positioning systems. The module exhibits disturbance vibration that is difficult to control because the air bearings have too small a damping coefficient. In this paper, an eddy-current damper (ECD) is proposed for an air bearing-guided linear motion module to improve the vibration isolation characteristics. A Halbach magnet array is devised to increase the density of the magnetic flux of the ECD because a stronger magnetic field generates a greater damping force. A theoretical magnetic model of a Halbach magnet array is presented, and its working principle is investigated. In order to investigate the performance of the module, an experimental instrument with the module, ECD, and control devices was constructed. The authors compared the experimental data of the module’s positioning performance for the cases with and without the ECD.