We aim to address a new task named few-shot early action prediction (FS-EAP) that learns classifiers for novel actions from only a few partially observed videos. We argue that the task is extremely challenging since the partially observed videos do not contain enough action information in a few-shot environment. To tackle this task, in this paper, we propose a scene-aware spatio-temporal graph neural network (SA-STGNN) by leveraging the fine-grained spatio-temporal interactions in the video scenes. Specifically, we first generate a spatio-temporal graph corresponding to the partially observed video to capture comprehensive spatio-temporal correlations. Then we utilize the spatio-temporal graph as the input of our SA-STGNN and predict the augmented video features corresponding to the complete video. The architecture uses several scene-aware learning blocks, which are a combination of edge fusion graph neural layers and temporal gated convolutional layers to jointly model spatial and temporal dependencies. Finally, we employ an early action predictor to exploit the learned video features for predicting actions in the few-shot setting. Extensive experimental results on two widely adopted video datasets demonstrate the effectiveness of our approach and its superior performance over the state-of-the-art approaches.