Measurements of the single-photoionization cross-section of Cu-like Zn+ ions are reported in the energy (wavelength) range 17.5 eV (708 Å) to 90 eV (138 Å). The measurements on this trans-Fe element were performed at the Advanced Light Source synchrotron radiation facility in Berkeley, California at a photon energy resolution of 17 meV using the photon-ion merged-beams end-station. Below 30 eV, the spectrum is dominated by excitation autoionizing resonance states. The experimental results are compared with large-scale photoionization cross-section calculations performed using a Dirac Coulomb R-matrix approximation. Comparisons are made with previous experimental studies, resonance states are identified and contributions from metastable states of Zn+ are determined.