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CaKFe₄As₄ is a member of the iron arsenide superconductors in which partial substitution of Ni for Fe shifts the ground state from superconducting to antiferromagnetically (AFM) ordered. Employing neutron diffraction we determined that the AFM order is a non-collinear, commensurate structure with a hedgehog spin-vortex crystal (SVC) arrangement in the Fe planes and a simple AFM stacking perpendicular to them. The long-range SVC order coexists with superconductivity, however, similar to the doped 122 compounds with collinear stripe AFM, the ordered magnetic moment is gradually suppressed as the superconducting order parameter develops. Almost complete suppression of the AFM order is observed in a sample close to the critical Ni concentration, resulting in a back-bending of the AFM-transition-temperature phase line as a function of concentration. This supports the notion that both collinear and non-collinear magnetism as well as superconductivity compete for the same Fermi-surface nested electrons in the iron arsenide superconductors.