We propose a Uzawa block relaxation domain decomposition method for a two-body contact problem with Tresca friction. We introduce auxiliary interface unknowns to transform the variational problem into a saddle-point problem. Applying a Uzawa block relaxation algorithm to the corresponding augmented Lagrangian functional we obtain a domain decomposition algorithm in which we have to solve two uncoupled linear elasticity subproblems in each iteration. The auxiliary unknowns are computed explicitly using Kuhn-Tucker conditions and Fenchel duality theory. Numerical experiments show the scalability of the domain decomposition algorithm on matching or nonmatching meshes for two- or three-dimensional contact problems.