In recent years, deep learning-based drug-target affinity (DTA) prediction has emerged as a critical technology in drug discovery. A key aspect of this process is the feature interaction between drugs and targets. However, most existing deep learning models lack effective feature interactions during the feature extraction process, and their ability to model long-range dependencies is limited, resulting in constrained model performance. To address these issues, we propose a feature interaction module called CroMamba, which facilitates progressive feature interaction by combining partial cross-attention with the Mamba mechanism. Subsequently, we developed an affinity prediction architecture named CroMamba-DTA by integrating convolutional neural networks, Mamba, and CroMamba. Experimental results demonstrate that CroMamba-DTA significantly enhances the generalization ability and stability of the model in experimental settings involving both New-drug and New-target settings compared to state-of-the-art models. Additionally, we conducted extensive ablation experiments to demonstrate the contributions of CroMamba and other key modules to the model's generalization ability. Furthermore, we validated the model's capacity to identify critical binding sites through a case study visualization.