We present the first nuclear cross-section measurements of (p,γ) and (p,n) reactions on ^{118}Te at energies relevant for the γ-process nucleosynthesis. Absolute cross-section values for center-of-mass energies of 6, 7 and 10 MeV are provided, together with a theoretical extrapolation to the Gamow window. This experiment marks the first time that direct proton-induced reactions have been measured on a radioactive ion beam at the Experimental Storage Ring (ESR) at GSI, Darmstadt. This paves the way for a large variety of measurements, delivering new constraints for explosive nucleosynthesis and for physics beyond nuclear stability.