Echo State Networks (ESNs) are a powerful tool for sequential time series prediction and classification, leveraging reservoir computing to model complex temporal dynamics with minimal training effort. This paper presents a privacy-preserving framework for Echo State Networks using homomorphic encryption (HE) to enable secure time series prediction without compromising data confidentiality. The proposed CryptoESN model performs all computations on encrypted data, ensuring end-to-end privacy throughout the inference process. We evaluate the approach on the benchmark Mackey-Glass time series dataset, comparing the predictive performance of the standard ESN and CryptoESN across multiple time delays. Experimental results demonstrate that CryptoESN achieves prediction accuracy comparable to the standard ESN, with only a slight increase in error metrics such as MSE, NRMSE, MAPE, and MAE. For instance, with a time delay of \(\tau =17\) , CryptoESN reports an MSE of 0.0014 versus 0.0012 for the standard ESN, and for \(\tau =30\) , MSE values are 0.0032 and 0.0024, respectively. These results illustrate that combining HE with ESNs allows for strong privacy protection and consistent forecasting performance, which is considered the framework for sensitive time series applications.