For a variety of applications within power systems, the precision of data acquisition is of paramount importance. However, the actual data may be corrupted by noise in the process of measurement or transmission, and the accuracy of dynamic security assessment (DSA) will be affected. In light of the poor interpretability exhibited by traditional machine learning (ML) methods in denoising, a physics-informed denoising model (PIDM) for dynamic data recovery is proposed. The differential equations of physical models in power systems are employed to guide the training of PIDM. They are transformed into physical constraints and subsequently incorporated into the loss function of stacked denoising autoencoder (SDAE) to cleanse noisy data. By integrating the powerful learning capabilities of ML with the rigorous constraints of physical laws, the noisy data recovered by PIDM can better satisfy the dynamic equations. Consequently, a more pronounced denoising effect can be achieved. The improvement of the PIDM over common ML-based models is explored when dealing with the noisy data with varying degrees of interference or those of unexpected faults. The effectiveness is validated through simulation results in IEEE 39-bus system and the East China power grid. The results show that this method can reduce the total mean square error (MSE) of the recovery of noisy data to at least 65.27% of that of the traditional methods under the same conditions. In addition to demonstrating superior denoising performance, the generalization capability under diverse noise conditions is also deemed excellent.