This paper presents a physics-informed deep learning framework for the reconstruction of full scattered spatiotemporal Lamb wavefields (video images) in plate-like structures from a sparse set of time-series sensor data. The reconstructed scattered wavefield contains a wealth of information about the wave propagation phenomenon including any interactions of the propagating wave with damage in the structure. This information is paramount for damage diagnosis as is demonstrated in this paper via impact diagnosis—a key structural health monitoring application. A physics-informed neural network (PINN) that encodes the underlying elastodynamic field equations into the learning/training process in the neural network is proposed for this purpose. This prior wavefield physics knowledge embedded in the loss function acts as a regularization agent for the minimization problem in the neural network training, thereby enabling the extrapolation of a sparse set of one-dimensional time-series signals into two-dimensional scattered wavefield. The wavefield reconstruction capabilities of the proposed supervised forward PINN framework are first verified both numerically and experimentally for a stiffened aluminum panel under a couple of narrowband ultrasonic-frequency excitations, and the results confirm its robustness to low spatial resolution and substantial noise in the measured sensor data. The PINN requires far fewer sensors for scattered wavefield reconstruction, thereby permitting for a higher sensor spacing or lower spatial sampling. To this end, it is shown that a sensor spacing of 5λ generates good wavefield reconstruction accuracy, which is a 10-fold increase over the Nyquist–Shannon sampling limit (λ/2). Two sets of experiments are then conducted on a long-stiffened aluminum panel to validate the proposed framework via low-velocity impact diagnosis in the near-ultrasonic frequency range. The first set of experiments, with the known excitation force incorporated into the PINN, allows the wavefields to be accurately reconstructed with the sensor spacing up to 5λ as expected. The second set of experiments assumes unknown impact force history—a classical case of impact diagnosis where the impact force history is not known a priori. It is shown that the wavefield reconstruction through PINN still provides good accuracy albeit with a less generous sensor spacing of 2λ. A convolutional neural network long short-term memory (CNN-LSTM) model then solves the mathematically inverse problem of inferring the impact location and impact force history by analyzing the reconstructed impact generated wavefield. The impact location is predicted well with 93% accuracy, and the impact force history is reconstructed with 90% accuracy, further validating the proposed framework.