  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.
