The majority of High Mass X-ray Binaries (HMXBs) behave like X-ray pulsars, revealing that they contain a magnetised neutron star. Among the four HMXBs showing neither pulsations nor the characteristics of accreting black holes, there is the unusual HMXB 4U 2206+54. Here we present contemporaneous high-energy and radio observations of this system conducted with INTEGRAL and the VLA, in order to unveil its nature. The high-energy spectra show clear indications of the presence of an absorption feature at ~32 keV. This is the third high-energy observatory to reveal marginal evidence of this feature, giving strong support to the existence of a cyclotron resonance scattering feature, which implies a magnetic field of 3.6× 1012 G. On the other hand, the source is not detected at centimetre radio wavelengths with a 3σ upper limit of 0.039 mJy. The expected radio emission for an accreting black hole in the low/hard state, inferred from X-ray flux measurements, would be at least 60 times greater than the measured upper limit. Both results firmly indicate that, in spite of the absence of pulsations, 4U 2206+54 hosts a magnetic accreting neutron star, the first one not to be observed as an X-ray pulsar.