14 LaTeX pages, 6 figures.A renormalizable coupling between the Higgs and a scalar unparticle operator O_U of non-integer dimension d_U < 2 gives rise, after electroweak symmetry breaking, to a mass gap in the unparticle continuum and a shift in the original Higgs mass, which can end up above or below the mass gap. We show that, besides the displaced Higgs state, a new isolated state can generically appear in the spectrum near or below the mass gap. Such state (which we call phantom Higgs) is a mixture of Higgs and unparticles and therefore has universally reduced couplings to fermions and gauge bosons. This phenomenon could cause the mass of the lightest Higgs state accessible to colliders to be much smaller than the mass expected from the SM Lagrangian.Work supported in part by the European Commission under the European Union through the Marie Curie Research and Training Networks “Quest for Unification” (MRTN-CT-2004-503369) and “UniverseNet” (MRTN-CT-2006-035863); by the Spanish Consolider-Ingenio 2010 Programme CPAN (CSD2007-00042); by a Comunidad de Madrid project (P-ESP-00346) and by CICYT, Spain, under contracts FPA 2007-60252 and FPA 2005-02211.