A deformation-induced phase transformation in a face-centered cubic (FCC) Co20Cr26Fe20Mn20Ni14 high-entropy alloy during cryogenic high-pressure torsion (HPT) discovered in this work is reported. Thermodynamic calculations prove that in the Co20Cr26Fe20Mn20Ni14 alloy, a hexagonal close-packed (HCP) phase is stable at low temperatures. Microstructural and compositional analyses suggest that a diffusionless deformation-induced FCC-to-HCP phase transformation occurred during cryogenic HPT.