This work addresses the development of a physics-informed Long Short-Term Memory (LSTM) network for fluid-structure interaction (FSI) problems. The LSTM-based Recurrent Neural Network (RNN) is a variant of the deep learning approach that includes the memory effect in its network. Therefore, it is very convenient for developing a surrogate model for unsteady physical phenomena. The physics-informed LSTM network (LSTM-PINN) is constructed by incorporating the underlying physics of the process to modify the loss function with governing equations in discretized form. The LSTM-PINN algorithm is applied to an oscillating pitching and plunging airfoil with two degrees of freedom immersed in an incompressible flow. The fluid part of the problem is governed by incompressible Navier Stokes equation and structural part is governed by rigid-body dynamics equations. As the number of degrees of freedom of the system increases, the dimensionality of the system is first reduced using the Discrete Empirical Interpolation Method (DEIM) and then the LSTM-PINN algorithm is applied to the reduced system (DEIM-LSTM-PINN network). The motivation of the current work is to couple an external CFD solver with the existing physics-informed neural network framework to enable LSTM netwrok learn governing dynamics when a sparse training dataset is available.