Obtaining an accurate prediction of the number of influenza patients in specific areas is a crucial task undertaken by medical institutions. Infections (such as influenza) spread from person to person, and people are rarely confined to a single area. Therefore, creating a regional influenza prediction model should consider the flow of people between different areas. Although various regional flu prediction models have previously been proposed, they do not consider the flow of people among areas. In this study, we propose a method that can predict the geographical distribution of influenza patients using commuting data to represent the flow of people. To elucidate the complex spatial dependence relations, our model uses an extension of the graph convolutional network (GCN). Additionally, a prediction interval for medical institutions is proposed, which is suitable for cyclic time series. Subsequently, we used the weekly data of flu patients from health authorities as the ground-truth to evaluate the prediction interval and performance of influenza patient prediction in each prefecture in Japan. The results indicate that our GCN-based model, which used commuting data, considerably improved the predictive accuracy over baseline values both temporally and spatially to provide an appropriate prediction interval. The proposed model is vital in practical settings, such as in the decision making of public health authorities and addressing growth in vaccine demand and workload. This paper primarily presents a GCN as a useful means for predicting the spread of an epidemic.