Composite material prepared by spark plasma sintering (SPS) from a powder mixture of AlCrFeSi rapidly solidified alloy and 5 wt. % of Ni particles was studied in this work. It was proven that during SPS compaction at 500 °C, no intermetallic phases formed on the surface of Ni particles. The material exhibited sufficient mechanical properties obtained by tensile testing (ultimate tensile stress of 203 ± 4 MPa, ductility of 0.8% and 0.2% offset yield strength of 156 ± 2 MPa). Tensile samples were pre-stressed to 180 MPa and annealed at 450 and 550 °C for 1 h. Annealing at 450 °C did not lead to any recovery of the material. Annealing at 550 °C caused the full recovery of 0.2% offset yield strength, while the ductility was decreased. The self-healing behaviour originates from the growth of intermetallic phases between the Ni particle and the Al matrix. The sequence of NiAl, Ni2Al3 and NiAl3 intermetallic phases formation was observed. In particular, the morphology of the NiAl3 phase, growing in thin dendrites into the Al matrix, is suitable for the closing of cracks, which pass through the material.