Understanding protein-metal interactions is central to structural biology, with metal ions being vital for catalysis, stability, and signal transduction. Predicting metal-binding residues and metal types remains challenging due to the structural and evolutionary complexity of proteins. Conventional sequence- and structure-based methods often fail to capture co-evolutionary constraints that reflect how residues evolve together to maintain metal-binding functionality. Recent co-evolution-based methods capture part of this information, but still underutilize the complete co-evolved residue network. To address this limitation, we introduce the Metal-Binding Graph Neural Network (MBGNN), which leverages the complete co-evolved residue network to better capture complex dependencies within protein structures. Experimental results show that MBGNN substantially outperforms the state-of-the-art co-evolution-based method MetalNet2, achieving F1 score improvements of 2.5% for binding residue identification and 3.3% for metal type classification on the MetalNet2 dataset. Its superiority is further demonstrated on both the MetalNet2 and MIonSite datasets, where it outperforms two co-evolution-based and two sequence-based methods, achieving the highest mean F1 scores across both prediction tasks. These findings highlight how integrating co-evolutionary residue networks with graph-based learning advances our ability to decode protein-metal interactions, thereby facilitating functional annotation and rational metalloprotein design. The code and data are released at https://github.com/SRastegari/MBGNN.