This packaging for sterile products or products intended to be sterilized by a gas, for example a gas of the ETO type, comprises a tub (2) made of plastic and a cover sheet (14) made of selectively impervious material, fixed to the tub (2) so as to seal the latter imperviously.According to the invention, the packaging comprises a screen (20, 22; 24, 26; 26) against electron radiation (E), placed along the cover sheet (14) on the inside of the tub (2) and dimensioned in such a way as to extend above the products (10) to be sterilized and so as to delimit on the cover sheet (14) a peripheral zone (14a) for fixing this cover sheet (14) to the tub (2).