Zero-shot anomaly detection (ZSAD) requires detection models trained using auxiliary data to detect anomalies without any training sample in a target dataset. It is challenging since the models need to generalize to anomalies across different domains. Recently, CLIP-based anomaly detection methods, such as WinCLIP and AnomalyCLIP, have demonstrated superior performance in the ZSAD task, due to the strong zero-shot recognition of the CLIP model. However, they overlook the utilization of frequency information of images. In this paper, we find that frequency information could benefit the ZSAD task, since some properties of the anomaly area, such as appearance defects, can also be reflected based on its frequency information. To this end, We propose Frequency Enhanced CLIP (FE-CLIP), taking advantage of two different but complementary frequency-aware clues, (1) Frequency-aware Feature Extraction adapter, and (2) Local Frequency Statistics adapter, in the visual encoder of CLIP, to deeply mine frequency information for the ZSAD task. We apply DCT as the frequency-domain transformation. Through comprehensive experiments, we show that the proposed FE-CLIP has good generalization across different domains and achieves superior zero-shot performance of detecting and segmenting anomalies in 10 datasets of highly diverse class semantics from various defect inspections and medical domains. Besides, the proposed FE-CLIP also achieves superior performance under the few-normal-shot anomaly detection settings. Codes will be open-sourced after being accepted.