Irregularly Sampled Medical Time Series (ISMTS) are commonly found in the healthcare domain, where different variables exhibit unique temporal patterns while interrelated. However, many existing methods fail to efficiently consider the differences and correlations among medical variables together, leading to inadequate capture of fine-grained features at the variable level in ISMTS. We propose Knowledge-Empowered Dynamic Graph Network (KEDGN), a graph neural network empowered by variables' textual medical knowledge, aiming to model variable-specific temporal dependencies and inter-variable dependencies in ISMTS. Specifically, we leverage a pre-trained language model to extract semantic representations for each variable from their textual descriptions of medical properties, forming an overall semantic view among variables from a medical perspective. Based on this, we allocate variable-specific parameter spaces to capture variable-specific temporal patterns and generate a complete variable graph to measure medical correlations among variables. Additionally, we employ a density-aware mechanism to dynamically adjust the variable graph at different timestamps, adapting to the time-varying correlations among variables in ISMTS. The variable-specific parameter spaces and dynamic graphs are injected into the graph convolutional recurrent network to capture intra-variable and inter-variable dependencies in ISMTS together. Experiment results on four healthcare datasets demonstrate that KEDGN significantly outperforms existing methods.