Providing an early warning of galactic supernova explosions from neutrino signals is important in studying supernova dynamics and neutrino physics. A dedicated supernova trigger system has been designed and installed in the data acquisition system at Daya Bay and integrated into the worldwide Supernova Early Warning System (SNEWS). Daya Bays unique feature of eight identically-designed detectors deployed in three separate experimental halls makes the trigger system naturally robust against cosmogenic backgrounds, enabling a prompt analysis of online triggers and a tight control of the false-alert rate. The trigger system is estimated to be fully sensitive to 1987A-type supernova bursts throughout most of the Milky Way. The significant gain in sensitivity of the eight-detector configuration over a mass-equivalent single detector is also estimated. The experience of this online trigger system is applicable to future projects with spatially distributed detectors.