Metal–matrix composites (MMC) of aluminium alloy 7075 (AA7075) containing 1 wt.% and 0.5 wt.% multiwall carbon nanotubes (MWCNTs) were developed by powder metallurgy, using a high energy ball milling (HEBM) process for dispersion of the MWCNTs. The powder of the AA7075-MWCNT obtained was characterized by X-ray diffraction (XRD) and scanning electron microscopy (SEM). The microstructural changes produced during the milling process, such as the modification of the crystallite size, as well as the micro-deformation of the matrix crystal lattice, were determined using the Scherrer formula. After consolidation into a strip shape using the hot powder extrusion (HPE) process at 500 °C, no porosity was detected and a fine homogeneous dispersion of the reinforcement into the matrix was obtained. After performing a 0.2 HV test and tensile tests in the extruded profiles of both composites, a better combination of properties was found in samples of AA7075-0.5 wt.% MWCNT, with the increase in measured ductility being especially remarkable.