A turbomachine blade or vane of composite material comprising fiber reinforcement densified by a matrix is fabricated by a method comprising: making a one-piece fiber blank by three-dimensional weaving; shaping the fiber blank to obtain a one-piece fiber preform having a first portion forming a blade airfoil and root preform and at least one second portion forming a blade platform preform; and densifying the preform with a matrix to obtain a composite material blade or vane having fiber reinforcement constituted by the preform and densified by the matrix, forming a single part with at least one incorporated platform.