It has long been suspected that magnetism could play a vital role in the phase stability of multicomponent high-entropy alloys. However, the nature of the magnetic order, if any, has remained elusive. Here, by using elastic and inelastic neutron scattering, we demonstrate evidence of antiferromagnetic order below ∼80 K and strong spin fluctuations persisting to room temperature in a single-phase face-centered cubic (fcc) CrMnFeCoNi high-entropy alloy. Despite the chemical complexity, the magnetic structure in CrMnFeCoNi can be described as γ-Mn-like, with the magnetic moments confined in alternating (001) planes and pointing toward the ⟨111⟩ direction. Combined with first-principles calculation results, it is shown that the antiferromagnetic order and spin fluctuations help stabilized the fcc phase in CrMnFeCoNi high-entropy alloy.