In-beam γ-ray spectroscopy of ^{79}Cu is performed at the Radioactive Isotope Beam Factory of RIKEN. The nucleus of interest is produced through proton knockout from a ^{80}Zn beam at 270 MeV/nucleon. The level scheme up to 4.6 MeV is established for the first time and the results are compared to Monte Carlo shell-model calculations. We do not observe significant knockout feeding to the excited states below 2.2 MeV, which indicates that the Z=28 gap at N=50 remains large. The results show that the ^{79}Cu nucleus can be described in terms of a valence proton outside a ^{78}Ni core, implying the magic character of the latter.