Resonant magnetic excitations are recognised as hallmarks of unconventional superconductivity in copper oxides, iron pnictides and heavy-fermion compounds. Model calculations have related these modes to the microscopic properties of the pair wave function, but the mechanisms of their formation are still debated. Here we report the discovery of a similar resonant mode in the non-superconducting antiferromagnetic heavy-fermion metal CeB6. Unlike conventional magnons, the mode is non-dispersive and is sharply peaked around a wave vector separate from those characterising the antiferromagnetic order. It is likely associated with a co-existing order parameter of the unusual antiferro-quadrupolar phase of CeB6, which has long remained hidden to neutron-scattering probes. The mode energy increases continuously below the onset temperature for antiferromagnetism, in parallel to the opening of a nearly isotropic spin gap throughout the Brillouin zone. These attributes are similar to those of the resonant modes in unconventional superconductors. This unexpected commonality between the two disparate ground states indicates the dominance of itinerant spin dynamics in the ordered low-temperature phases of CeB6 and throws new light on the interplay between antiferromagnetism, superconductivity and 'hidden' order parameters in correlated-electron materials.