Compressional wave velocity (P-wave) plays an important role in seismic amplitude versus offset (AVO) forward and inversion modeling and reservoir prediction. However, due to the high cost and difficulty of P-wave logging, the actual acquired P-wave data is limited, which generally does not suffice for practical applications. To provide reliable data support for oil and gas reservoir exploration, a P-wave prediction method under multi-source spatiotemporal feature fusion and physics-informed neural network (MSTFPIN) is proposed. First, a spatiotemporal hybrid model (STHN) is constructed by combining convolutional neural network (CNN) and bidirectional long short-term memory (BLSTM) neural network to accurately express the spatial and temporal characteristics of the logging curves, which utilizes the local perception ability of CNN and long short-term memory function of BLSTM to mine their local shape and depth trends. Then, seismic data are introduced as an additional input of multi-source information, which fills the gap of inter-well geological information, and feature fusion is used to fully exploit the information from multiple sources to enhance the available data. Finally, a physics-informed neural network (PINN) is constructed based on the idea of seismic forward modeling in petroleum engineering to guide the training process of the prediction model, which ensures that the prediction results are consistent with geological laws. P-wave prediction experiments are conducted using real logging and seismic data to verify the effectiveness and generalization ability of the proposed method compared with other methods. The experimental results show that the proposed MSTFPIN model exhibit better prediction performance, and the correlation coefficient and coefficient of determination reach 0.9619 and 0.9234, respectively. Compared with traditional empirical and regression models, the proposed MSTFPIN exhibited higher accuracy and generalization. Overall, our results demonstrate the proposed method can be implemented in real oil fields to improve the accuracy of reservoir prediction.