Magnon as a quantized spin wave has attracted extensive attention in various fields of physics, such as magnon spintronics, microwave photonics, and cavity quantum electrodynamics. Here, we explore theoretically the magnon chaos-order transition in cavity optomagnonics, which still remains largely unexplored in this emerging field. We find that the evolution of magnon experiences the transition from order to period-doubling bifurcation and finally enters chaos by adjusting the microwave driving power. Different from normal chaos, the magnon chaos-order transition proposed here is phase mediated. Beyond their fundamental scientific significance, our results will contribute to the comprehension of nonlinear phenomena and chaos in optomagnonical systems, and may find applications in chaos-based secure communication.