Wind turbines (WTs) are highly coupled systems, whose safe and efficient operation rely on the supervisory control and data acquisition (SCADA) system. Considering the limitations of sensor placement and practical engineering, some physical quantities cannot be directly acquired during the operation. As a result, the traditional data-driven methods often fail to model the complex operating conditions of WTs effectively due to the lack of relevant physical constraints. To address this issue, this paper proposes a physics-informed graph neural network (PIGNN) method for the WT condition monitoring. First, a graph structure is built by representing the coupling relationships among different WT components, then a graph neural network (GNN) is employed to learn spatiotemporal correlation features of SCADA data and capture the dynamic characteristics of WT. And then a physics-informed neural network (PINN) is embedded into the proposed framework, whose physics-based loss terms can express the physical relationships including power balance, torque balance, voltage balance, temperature constraints and operating boundary constraints. In this way, the physical prior knowledge could be integrated into the data-driven model effectively. Furthermore, an adaptive normalization strategy based on an exponential moving average is developed to address the magnitude inconsistency between the data fitting loss and the physics-based constraint losses. This could balance the magnitude difference of different loss terms and improve the stability of model training. Finally, the experiments are carried out on two real WT cases. Results show that the proposed PIGNN method can balance the data fitting objective and the physics-based constraint objective effectively while providing the high prediction accuracy. It could also improve the performance of anomaly detection and early warning, which verifies the effectiveness of physics-based constraint modeling for WT condition monitoring.