Graph neural networks (GNNs) have demonstrated impressive performance in a broad spectrum of fields, but always suffer from the generalization problem when confronted with out-of-distribution (OOD) scenarios. Information bottleneck (IB) principle, which endeavors to learn the minimally sufficient representations for downstream tasks, has been shown to be a promising strategy in dealing with this problem. However, the IB-based methods do not inherently distinguish between causal and non-causal parts in the graph, leading to underperforming OOD generalization ability. In this paper, we develop the Graph Causal Information Bottleneck (GCIB) framework, a causal extension of the IB for graph data, which is capable of jointly compressing abundant information and capturing causal dependency from the input graph. Specifically, we endow graph IB with the ability of maintaining causal control by incorporating the underlying causal structure and introducing intervention operation. On this basis, we formulate the learning objective for GCIB and present its specific implementation. Graph representations learned by GCIB can effectively preserve causal information that fundamentally determines graph properties, resulting in outstanding OOD generalization ability. Extensive experiments on both synthetic and real-world datasets demonstrate the superiority of GCIB over state-of-the-art baselines.