The COMET Phase-I experiment searches for a neutrinoless muon-to-electron conversion which has never been observed yet. The world's highest intensity muon beam is applied, and it leads to an unacceptable trigger rate of $\mathcal{O}(10^6)$ Hz. For stable data collection, the trigger rate must be reduced to $\mathcal{O}(10^3)$ Hz. This requirement is met using online event classification in the detector system which holds 99\% of signal events. This classification is performed by an FPGA-based trigger system, and its processing time is set to less than 5 $\mathrm{\mu s}$ by a buffer size of the detector readout electronics. A prototype board for the trigger system was developed, and communication systems for related electronics devices were also constructed. From test results, the total processing time is estimated to be 2.8 $\mathrm{\mu s}$, which meets the requirement. We have also developed an online self-trigger system for cosmic-rays and confirmed the feasibility of this hardware logic. The trigger electronics were installed in a setup for cosmic-ray measurement, and the data acquisition was successfully done using the self-trigger system.