We observed the cluster CIZA J2242.8+5301 with the Arcminute Microkelvin Imager at 16 GHz and present the first high radio-frequency detection of diffuse, non-thermal cluster emission. This cluster hosts a variety of bright, extended, steep-spectrum synchrotron-emitting radio sources, associated with the intracluster medium, called radio relics. Most notably, the northern, Mpc-wide, narrow relic provides strong evidence for diffusive shock acceleration in clusters. We detect a puzzling, flat-spectrum, diffuse extension of the southern relic, which is not visible in the lower radio-frequency maps. The northern radio relic is unequivocally detected and measures an integrated flux of 1.2 ± 0.3 mJy. While the low-frequency (<2 GHz) spectrum of the northern relic is well represented by a power law, it clearly steepens towards 16 GHz. This result is inconsistent with diffusive shock acceleration predictions of ageing plasma behind a uniform shock front. The steepening could be caused by an inhomogeneous medium with temperature/density gradients or by lower acceleration efficiencies of high energy electrons. Further modelling is necessary to explain the observed spectrum.