Measurements of the single photoionization cross section of Cu-like Zn$^+$ ions are reported in the energy (wavelength) range 17.5 eV (709 AA) to 90 eV (138 AA). The measurements on this {it 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. Comparison are made with previous experimental studies, resonance states are identified and contributions from metastable states of Zn$^+$ determined.