We present broad-band photometry of five transits in the planetary system WASP-36, totaling 17 high-precision light curves. Four of the transits were simultaneously observed in four passbands (g', r', i', z'), using the telescope-defocussing technique, and achieving scatters of less than 1 mmag per observation. We used these data to improve the measured orbital and physical properties of the system, and obtain an optical transmission spectrum of the planet. We measured a decreasing radius from bluer to redder passbands with a confidence level of more than 5 sigma. The radius variation is roughly 11 pressure scale heights between the g' and the z' bands. This is too strong to be Rayleigh scattering in the planetary atmosphere, and implies the presence of a species which absorbs strongly at bluer wavelengths.