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Large vision-language models such as CLIP have made significant strides in zero-shot anomaly detection through prompt engineering. However, most existing methods typically process each test image individually, ignoring the practical rarity of abnormal patches in real-world scenarios. Although some batch-based approaches exploit the rarity by processing multiple samples concurrently, they generally introduce unacceptable latency for real-time applications. To mitigate these limitations, we propose RareCLIP, a novel online zero-shot anomaly detection framework that enables sequential image processing in real-time without requiring prior knowledge of the target domain. RareCLIP capitalizes on the zero-shot capabilities of CLIP and integrates a dynamic test-time rarity estimation mechanism. A key innovation of our framework is the introduction of a prototype patch feature memory bank, which aggregates representative features from historical observations and continuously updates their corresponding rarity measures. For each incoming image patch, RareCLIP computes a rarity score by aggregating the rarity measures of its nearest neighbors within the memory bank. Moreover, we introduce a prototype sampling strategy based on dissimilarity to enhance computational efficiency, as well as a similarity calibration strategy to enhance the robustness of rarity estimation. Extensive experiments demonstrate that RareCLIP attains state-of-the-art performance with 98.2% image-level AUROC on MVTec AD and 94.4% on VisA, while achieving a latency of 59.4 ms. Code is available at https://github.com/hjf02/RareCLIP.