This paper investigates the formation control problem of heterogeneous discrete-time nonlinear multi-agent systems with structural uncertainties. The control objective is to make the outputs of agents reach a desired formation while tracking a leader. The formation control problem of heterogeneous discrete-time multi-agent systems is first converted into a robust output regulation problem, and then, a distributed formation control scheme based on output regulation framework is proposed. A $p$-copy internal model is synthesized into the distributed formation control law such that the overall closed-loop system can be robust to structural uncertainties. It is shown that the heterogeneous discrete-time nonlinear multi-agent system can reach the desired formation regardless of small parameter permutations of agents under the proposed control law. Finally, simulation and experiment studies are provided to demonstrate the effectiveness of the proposed control law.