The Muon g-2 Experiment at Fermilab (E989) will measure the muon magnetic anomaly with unprecedented precision (0.14 ppm), which yields a factor of 4 improvement with respect to the previous measurements at Brookhaven National Laboratory (BNL) (E821). To achieve this goal, the relative response of each calorimeter channel must be calibrated and monitored at a level better than $10^{-3}$ in the time window of the muon fill. The calibration system uses a laser source and photodetectors. The data acquisition (DAQ) of the system is designed around two field-programmable gate array (FPGA)-based boards and a custom crate bus. The front-end board manages the photodetector operation and signal processing and performs a first-level data concentratio...