The level structure of neutron-deficient Zn-58 has been extracted experimentally. This nucleus is important for the rapid proton-capture process. Zn-58 was produced by using a (d,n)-type transfer reaction on Cu-57 in inverse kinematics at beam energies of 75 MeV/u. Several gamma-ray transitions have been identified. The experiment utilized the state-of-the-art GRETINA gamma-ray energy tracking array in conjunction with the large-acceptance spectrometer S800 at NSCL. The excitation energies of the identified low-lying states in Zn-58 are important for constraining the Cu-57(p,gamma)Zn-58 reaction rate under X-ray burst conditions.