Recently, the neural-network-based reduced-order modeling techniques have attracted attention due to their performance in reducing the number of calculation dimensions for simulating turbulent flow fields in which advection is predominant; that is, non-linearity is prominent. Murata et al. used a convolutional neural network (CNN) to perform non-linear dimensional reduction for a two-dimensional flow field around a circular cylinder (Re=100) and reproduce the original flow field using only two nonlinear modes. We extend this technique to a three-dimensional flow field, and constructed a reduced-order model by the massively parallel distributed machine learning. Specifically, this method was implemented as the scalable distributed learning framework on Supercomputer Fugaku. This study demonstrates that our model can significantly (several orders of magnitude) reduce the computational cost of reproducing the large-scale vortex structure of the turbulent three-dimensional flow (Re=8.2×10^6). Furthermore, we show the reproduction performance of our model in resolving the short cycle (empirically known to be around 100Hz) fluctuation around the vehicle body with increasing the number of decomposing modes. In addition, we demonstrate that the computational performance of our method scales well to about tens of thousands of nodes (i.e., millions of cores) on Fugaku while increasing the number of network parameters.