A method of fabricating a multi-perforated part out of composite material includes positioning a sand-blasting mask on a preform including a fiber texture impregnated with a polymerized ceramic-precursor resin, the mask having a plurality of openings corresponding to the perforations to be made in the preform; projecting abrasive particles at high speed against the surface of the mask so as to perforate the preform exposed in the openings of the mask; and pyrolyzing the multi-perforated preform so as to form a ceramic matrix in the multi-perforated fiber texture.