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Generating speech-consistent body and gesture movements is a long-standing problem in virtual avatar creation. Previous studies often synthesize pose movement in a holistic manner, where poses of all joints are generated simultaneously. Such a straightforward pipeline fails to generate fine-grained co-speech gestures. One observation is that the hierarchical semantics in speech and the hierarchical structures of human gestures can be naturally described into multiple granularities and associated together. To fully utilize the rich connections between speech audio and human gestures, we propose a novel framework named Hierarchical Audio-to-Gesture (HA2G) for co-speech gesture generation. In HA2G, a Hierarchical Audio Learner extracts audio representations across semantic granularities. A Hierarchical Pose Inferer subsequently renders the entire human pose gradually in a hierarchical manner. To enhance the quality of synthesized gestures, we develop a contrastive learning strategy based on audio-text alignment for better audio representations. Extensive experiments and human evaluation demonstrate that the proposed method renders realistic co-speech gestures and outperforms previous methods in a clear margin. Project page: https://alvinliu0.github.io/projects/HA2G