Surface roughness is a key indicator of the quality of mechanical products, which can precisely portray the fatigue strength, wear resistance, surface hardness and other properties of the products. The convergence of current machine-learning-based surface roughness prediction methods to local minima may lead to poor model generalization or results that violate existing physical laws. Therefore, this paper combined physical knowledge with deep learning to propose a physics-informed deep learning method (PIDL) for milling surface roughness predictions under the constraints of physical laws. This method introduced physical knowledge in the input phase and training phase of deep learning. Data augmentation was performed on the limited experimental data by constructing surface roughness mechanism models with tolerable accuracy prior to training. In the training, a physically guided loss function was constructed to guide the training process of the model with physical knowledge. Considering the excellent feature extraction capability of convolutional neural networks (CNNs) and gated recurrent units (GRUs) in the spatial and temporal scales, a CNN–GRU model was adopted as the main model for milling surface roughness predictions. Meanwhile, a bi-directional gated recurrent unit and a multi-headed self-attentive mechanism were introduced to enhance data correlation. In this paper, surface roughness prediction experiments were conducted on the open-source datasets S45C and GAMHE 5.0. In comparison with the results of state-of-the-art methods, the proposed model has the highest prediction accuracy on both datasets, and the mean absolute percentage error on the test set was reduced by 3.029% on average compared to the best comparison method. Physical-model-guided machine learning prediction methods may be a future pathway for machine learning evolution.