For the first time, we observed the emission of hot exozodiacal dust in L band. We used the new instrument MATISSE at the Very Large Telescope Interferometer to detect the hot dust around κ Tuc with a significance of 3σ to 6σ at wavelengths between 3.37 and 3.85μm and a dust-to-star flux ratio of 5 to 7 per cent. We modelled the spectral energy distribution based on the new L band data alone and in combination with H band data published previously. In all cases we find 0.58μm grains of amorphous carbon to fit the κ Tuc observations the best, however, also nanometre or micrometre grains and other carbons or silicates reproduce the observations well. Since the H band data revealed a temporal variability, while our Lband data were taken at a different epoch, we combine them in different ways. Depending on the approach, the best fits are obtained for a narrow dust ring at a stellar distance in the 0.1–029 au range and thus with a temperature between 940 and 1430K. Within the 1σ uncertainty dust location and temperature are confined to 0.032−1.18au and 600−2000K
