Incorporation of plasmonic nanostructures in the design of photoconductive devices (PCDs) has significantly improved their optical-to-terahertz conversion efficiency. However, this improvement comes at the cost of increased complexity for the design and simulation of these devices. Indeed, accurate and efficient modeling of multiphysics processes and intricate device geometries of nanostructured PCDs is challenging due to the high computational cost resulting from multiple characteristic scales in time and space. In this work, a discontinuous Galerkin (DG)-based unit-cell scheme for efficient simulation of PCDs with periodic nanostructures is proposed. The scheme considers two physical stages of the device and models them using two coupled systems: a system of Poisson and drift-diffusion equations describing the nonequilibrium steady state, and a system of Maxwell and drift-diffusion equations describing the transient stage. A "potential-drop" boundary condition is enforced on the opposing boundaries of the unit cell to mimic the effect of the bias voltage. Periodic boundary conditions are used for carrier densities and electromagnetic fields. The unit-cell model described by these coupled equations and boundary conditions is discretized using DG methods. Numerical results demonstrate that the proposed DG-based unit-cell scheme has the same accuracy in predicting the THz photocurrent as the DG framework that takes into account the whole device, while it significantly reduces the computational cost.