The Muon $g-2$ experiment, E989, is currently taking data at Fermilab with the aim of reducing the experimental error on the muon anomaly by a factor of four and possibly clarifying the current discrepancy with the theoretical prediction. A central component of this four-fold improvement in precision is the laser calibration system of the calorimeters, which has to monitor the gain variations of the photo-sensors with a 0.04% precision on the short-term ($sim 1,$ms). This is about one order of magnitude better than what has ever been achieved for the calibration of a particle physics calorimeter. The system is designed to monitor also long-term gain variations, mostly due to temperature effects, with a precision below the per mille level. This article reviews the design, the implementation and the performance of the Muon $g-2$ laser calibration system, showing how the experimental requirements have been met.
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