The invention relates to a process for producing a ceramic matrix composite (CMC) part by infiltration of a suspension (S) of a ceramic powder into a fibrous reinforcement (14). A suspension (S) of ceramic powder containing particles of chosen particle size, dispersed in at least one solvent, is prepared. The infiltration of the suspension is carried out in a single step in the fibrous reinforcement (14) positioned between a mold (12) and a permeable membrane (16), which makes it possible to apply a vacuum (V) and to subsequently remove the solvent from the suspension through the permeable membrane (16). The invention applies to the production of large-sized parts of complex shape, in particular in the field of aeronautics and aerospace engineering.