We have studied the interstellar extinction in a field of ∼3 arcmin × 3 arcmin at the core of the 30 Doradus nebula, including the central R 136 cluster, in the Large Magellanic Cloud. Observations at optical and near-infrared wavelengths, obtained with the WFC 3 camera on board the Hubble Space Telescope, show that the stars belonging to the red giant clump are spread across the colour–magnitude diagrams because of the considerable and uneven levels of extinction in this region. Since these stars share very similar physical properties and are all at the same distance, they allow us to derive the absolute extinction in a straightforward and reliable way. Thus, we have measured the extinction towards about 180 objects and the extinction law in the range 0.3–1.6 μm. At optical wavelengths, the extinction curve is almost parallel to that of the diffuse Galactic interstellar medium. Taking the latter as a template, the value of R V  = 4.5 ± 0.2 that we measure indicates that in the optical there is an extra grey component due to a larger fraction of large grains. At wavelengths longer than ∼1 μm, the contribution of this additional component tapers off as λ−1.5, like in the Milky Way, suggesting that the nature of the grains is otherwise similar to those in our Galaxy, but with a ∼2.2 times higher fraction of large grains. These results are consistent with the addition of ‘fresh’ large grains by supernova explosions, as recently revealed by Herschel and ALMA (Atacama Large Millimeter Array) observations of SN 1987A.