Dark photons are hypothetical massive vector particles that could mix with ordinary photons. The simplest theoretical model is fully characterised by only two parameters: the mass of the dark photon m$_{\gamma ^{\mathrm {D}}}$ and its mixing parameter with the photon, $\varepsilon $. The sensitivity of the SHiP detector is reviewed for dark photons in the mass range between 0.002 and 10 GeV. Different production mechanisms are simulated, with the dark photons decaying to pairs of visible fermions, including both leptons and quarks. Exclusion contours are presented and compared with those of past experiments. The SHiP detector is expected to have a unique sensitivity for m$_{\gamma ^{\mathrm {D}}}$ ranging between 0.8 and 3.3$^{+0.2}_{-0.5}$ GeV, and $\varepsilon ^2$ ranging between $10^{-11}$ and $10^{-17}$.