We report on the study of interstellar extinction across the Tarantula nebula (30 Doradus), in the Large Magellanic Cloud, using observations from the Hubble Tarantula Treasury Project in the 0.3 - 1.6 micron range. The considerable and patchy extinction inside the nebula causes about 3500 red clump stars to be scattered along the reddening vector in the colour-magnitude diagrams, thereby allowing an accurate determination of the reddening slope in all bands. The measured slope of the reddening vector is remarkably steeper in all bands than in the the Galactic diffuse interstellar medium. At optical wavelengths, the larger ratio of total-to-selective extinction, namely Rv = 4.5 +/- 0.2, implies the presence of a grey component in the extinction law, due to a larger fraction of large grains. The extra large grains are most likely ices from supernova ejecta and will significantly alter the extinction properties of the region until they sublimate in 50 - 100 Myr. We discuss the implications of this extinction law for the Tarantula nebula and in general for regions of massive star formation in galaxies. Our results suggest that fluxes of strongly star forming regions are likely to be underestimated by a factor of about 2 in the optical.