We studied the effect of friction stir processing (FSP) on the microstructure and properties of high-speed twin-roll cast strips made of an experimental Al–Mn–Cu–Be alloy. The samples were examined using light, scanning, and transmission electron microscopy, microchemical analysis, X-ray diffraction, and indentation testing. During FSP, the rotational speed varied, while other parameters remained constant. The uniformity of the microstructure increased with the growing rotational speed. In the stir zone, several processes took place, and the most important were: recrystallisation of the matrix grains, fragmentation of the primary intermetallic particles Al15Mn3Be2 and their more uniform distribution in the stir zone, fracture, and dispersion of the eutectic icosahedral quasicrystalline phase (IQC), transformation of tiny Al15Mn3Be2 and IQC particles into the τ1-Al26Mn6Cu4 phase and precipitation of Al–Mn–Cu precipitates. In the thermomechanically affected zone, new dislocations formed as well as dispersion of the IQC eutectic phase and recrystallisation of the matrix grains. In the heat-affected zone, dissolution of θ’-Al2Cu precipitates occurred. The hardness variation was not severe between the stir and heat-affected zones.