The construction of the three-dimensional Chern–Simons supergravity theory invariant under the minimal Maxwell superalgebra is presented. We obtain a supergravity action without cosmological constant term characterized by three coupling constants. We also show that the Maxwell supergravity presented here appears as a vanishing cosmological constant limit of a minimal AdS–Lorentz supergravity. The flat limit is applied at the level of the superalgebra, Chern–Simons action, supersymmetry transformation laws and field equations.