We derive precision predictions for the production of dark-matter particles recoiling against a jet with large transverse momentum at the LHC. The dark-matter fermions are described within a simplified model and couple to the Standard Model via a vector mediator. Our predictions for the mono-jet signature include the resummation of the leading and next-to-leading threshold logarithms. The corresponding matching coefficient is evaluated at NLO. The resummed result is matched to the fixed-order NLO cross section obtained from the MadGraph framework. We discuss numerical results for several benchmark scenarios at the LHC.