This paper proposes a physics-informed neural network (PINN) for predicting the early-age time-dependent behaviors of prestressed concrete beams. The PINN utilizes deep neural networks to learn the time-dependent coupling among the effective prestress force and the several factors that affect the time-dependent behavior of the beam, such as concrete creep and shrinkage, tendon relaxation, and changes in concrete elastic modulus. Unlike traditional numerical algorithms such as the finite difference method, the PINN directly solves the integro-differential equation without the need for discretization, offering an efficient and accurate solution. Considering the trade-off between solution accuracy and the computing cost, optimal hyperparameter combinations are determined for the PINN. The proposed PINN is verified through the comparison to the numerical results from the finite difference method for two representative cross sections of PSC beams.