Anxiety disorders impact millions globally, yet traditional diagnosis relies on clinical interviews, while machine learning models struggle with overfitting due to limited data. Large-scale data collection remains costly and time-consuming, restricting accessibility. To address this, we introduce the Hyperbolic Curvature Few-Shot Learning Network (HCFSLN), a novel Few-Shot Learning (FSL) framework for multimodal anxiety detection, integrating speech, physiological signals, and video data. HCFSLN enhances feature separability through hyperbolic embeddings, cross-modal attention, and an adaptive gating network, enabling robust classification with minimal data. We collected a multimodal anxiety dataset from 108 participants and benchmarked HCFSLN against six FSL baselines, achieving 88% accuracy, outperforming the best baseline by 14%. These results highlight the effectiveness of hyperbolic space for modeling anxiety-related speech patterns and demonstrate FSL's potential for anxiety classification.