A search for a narrow Higgs boson resonance in the diphoton mass spectrum is presented based on data corresponding to 7.0 fb{-1} of integrated luminosity from pp collisions at sqrt[s]=1.96 TeV collected by the CDF experiment. No evidence of such a resonance is observed, and upper limits are set on the cross section times branching ratio of the resonant state as a function of Higgs boson mass. The limits are interpreted in the context of the standard model and one fermiophobic benchmark model where the data exclude fermiophobic Higgs bosons with masses below 114 GeV/c{2} at a 95% Bayesian credibility level.