We have developed a photon detection system for muonic X-ray spectroscopy. The detector system consists of high-purity germanium detectors with BGO Compton suppressors. The signals from the detectors are readout with a digital acquisition system. The absolute energy accuracy, energy and timing resolutions, photo-peak efficiency, the performance of the Compton suppressor, and high count rate durability are studied with standard γ-ray sources and in-beam experiment using 27Al(p,γ)28Si resonance reaction. The detection system was demonstrated at Paul Scherrer Institute. A calibration method for a photon detector at a muon facility using muonic X-rays of 197Au and 209Bi is proposed.