During the first few nights following its discovery, we observed the interstellar Ca II and Na I lines towards supernova 1993J at high spectral resolution (full width half maximum (FWHM) approximately 5-6 km/s) with the William Herschel Telescope at La Palma. We find a crowd of absorption components in the radial-velocity range -135 km/s less than or equal to vlsr less than or equal to +165 km/s. In order to understand the origin of these features, we re-examined previous surveys of local interstellar gas, high-velocity gas, and intergalactic gas in the field. We also observed the line of sight of the supernova at 21 cm with the 100-m Radiotelescope of Effelsberg. We find that the components between +85 and +165 km/s originate in intergalactic gas within the M81 group of galaxies, tidally pulled out from one of the galaxies of the group. According to our analysis the gas at Vlsr approximately equal to -135 and -119 km/s originates within M81; its detection proves that the supernova is embedded in the inner region of that galaxy. The remaining components are produced in our Galaxy, including its halo.