Multivariate time series (MTS) forecasting endeavors to anticipate the forthcoming sequence of interdependent variables through the utilization of past observations. The prevailing methodologies, relying on deep neural networks, Transformer, or information bottleneck frameworks, persist in confronting challenges such as overlooking or inadequately capturing the inter / intra-series correlations evident in practical MTS datasets. In response to these challenges, we introduce a conditional information bottleneck-based strategy for MTS forecasting, grounded in information theory. Initially, we establish a conditional information bottleneck principle to capture the inter-series correlations via conditioning on non-target variables. Subsequently, a conditional mutual information-based technique is introduced to extract intra-series correlations by conditioning historical data, ensuring temporal consistency within each variable. Lastly, we devise a unified optimization objective and propose a training algorithm to collectively capture inter / intra-series correlations. Empirical investigations on authentic datasets underscore the superiority of our proposed approach over other cutting-edge competitors. Our code is available at https: //github.com/Xinhui-Lee/CIB-MTSF.