With advancements in renewable energy technologies, microgrids have evolved with distinctive cyber-physical system (CPS) characteristics, providing a dynamic and efficient control framework. However, the susceptibility of agents to false data injection attacks (FDIAs) during information transmission poses a notable security challenge. Existing efforts focus on detecting these attacks through machine learning methods, without regard to the cyber information embedded in the CPS communications. To address this gap, we propose a cyber-physical collaborative detection method (CPCGD) based on gate recurrent unit (GRU) and deep-learning neural network (DNN) to detect FDIAs, where the GRU is employed to capture temporal features in the physical domain, and the DNN is dedicated to capturing statistical features in the cyber domain. Moreover, a hierarchical detection and dynamic thresholding mechanism is presented to compensate for the poor performance of traditional distributed agents in microgrid environments. The experimental results and analysis demonstrate that the FDIA detection accuracy of the proposed scheme is better than several other benchmark detectors, and verify the effectiveness of the proposed scheme in cross-domain information detection.