We detect the kinematic Sunyaev-Zel'dovich (kSZ) effect with a statistical significance of 4.2σ by combining a cluster catalogue derived from the first year data of the Dark Energy Survey with cosmic microwave background temperature maps from the South Pole Telescope Sunyaev-Zel'dovich Survey. This measurement is performed with a differential statistic that isolates the pairwise kSZ signal, providing the first detection of the large-scale, pairwise motion of clusters using redshifts derived from photometric data. By fitting the pairwise kSZ signal to a theoretical template, we measure the average central optical depth of the cluster sample, $\bar{\tau }_e = (3.75 \pm 0.89)\times 10^{-3}$ . We compare the extracted signal to realistic simulations and find good agreement with respect to the signal to noise, the constraint on $\bar{\tau }_e$ , and the corresponding gas fraction. High-precision measurements of the pairwise kSZ signal with future data will be able to place constraints on the baryonic physics of galaxy clusters, and could be used to probe gravity on scales ≳100 Mpc.