As a member of the Gravitational wave high-energy Electromagnetic Counterpart All-sky Monitor (GECAM) constellation, GECAM-C is an all-sky gamma-ray monitor with in-flight trigger capability aboard the SATech-01 experimental satellite. Operating in a Sun-Synchronous Orbit, GECAM-C generates many in-flight triggers, some of which correspond to important astrophysical bursts, such as gamma-ray bursts and soft gamma-ray repeaters, which may require follow-up observations. However, there are also a substantial number of non-astrophysical triggers, such as particle events. Therefore, a prompt and accurate classification of in-flight triggers is essential for scientific research. In this work, we propose an automatic trigger classification algorithm for GECAM-C in-flight triggers with Bayesian inference. Applying this method to GECAM-C triggers from 2022 December to 2023 December, we demonstrate that it can successfully categorize all trigger types with an accuracy of about 95%, thereby providing effective support for rapid follow-up observations.