COVID-19 as a global pandemic causes a massive disruption to social stability that threatens human life and the economy. Policymakers and all elements of society must deliver measurable actions based on the pandemic's severity to minimize the detrimental impact of COVID-19. A proper forecasting system is arguably important to provide an early signal of the risk of COVID-19 infection so that the authorities are ready to protect the people from the worst. However, making a good forecasting model for infection risks in different cities or regions is not an easy task, because it has a lot of influential factors that are difficult to be identified manually. To address the current limitations, we propose a deep graph learning model, called PANDORA, to predict the infection risks of COVID-19, by considering all essential factors and integrating them into a geographical network. The framework uses geographical position relations and transportation frequency as higher-order structural properties formulated by higher-order network structures (i.e., network motifs). Moreover, four significant node attributes (i.e., multiple features of a particular area, including climate, medical condition, economy, and human mobility) are also considered. We propose three different aggregators to better aggregate node attributes and structural features, namely, Hadamard, Summation, and Connection. Experimental results over real data show that PANDORA outperforms the baseline method with higher accuracy and faster convergence speed, no matter which aggregator is chosen. We believe that PANDORA using deep graph learning provides a promising approach to get superior performance in infection risk level forecasting and help humans battle the COVID-19 crisis.