A process for manufacturing a metal part reinforced with ceramic fibers including machining at least one housing for an insert in a metal body having an upper face. At least one insert formed from ceramic fibers in a metal matrix is placed in the housing. The insert is covered with a cover. A vacuum is created in the interstitial space around the insert and the interstitial space is hermetically sealed under vacuum. The assembly, namely the metal body with the cover, is treated by hot isostatic pressure. The treated assembly is machined in order to obtain the part. The cover includes an element covering the insert in the slot and projecting from the upper face, and a sheet covering the upper face with said element. In particular, the insert is straight and the housing for the insert in the metal body forms a straight slot.