Time series imputation presents a significant challenge because it requires capturing the underlying temporal dynamics from partially observed time series data. Among the recent successes of imputation methods based on generative models, the information bottleneck (IB) framework offers a well-suited theoretical foundation for multiple imputations, allowing us to account for the uncertainty associated with the imputed values. However, directly applying the IB framework to time series data without considering their temporal context can lead to a substantial loss of temporal dependencies, which, in turn, can degrade the overall imputation performance. To address such a challenge, we propose a novel conditional information bottleneck (CIB) approach for time series imputation, which aims to mitigate the potentially negative consequences of the regularization constraint by focusing on reducing the redundant information conditioned on the temporal context. We provide a theoretical analysis of its effect by adapting variational decomposition. We use the resulting insight and propose a novel deep learning method that can approximately achieve the proposed CIB objective for time series imputation as a combination of evidence lower bound and novel temporal kernel-enhanced contrastive optimization. Our experiments, conducted on multiple real-world datasets, consistently demonstrate that our method significantly improves imputation performance (including both interpolation and extrapolation), and also enhances classification performance based on the imputed values.