Gamma-ray induced air showers are notable for their lack of muons, compared to hadronic showers. Hence, air shower arrays with large underground muon detectors can select a sample greatly enriched in photon showers by rejecting showers containing muons. IceCube is sensitive to muons with energies above similar to 500 GeV at the surface, which provides an efficient veto system for hadronic air showers with energies above 1 PeV. One year of data from the 40-string IceCube configuration was used to perform a search for point sources and a Galactic diffuse signal. No sources were found, resulting in a 90% C.L. upper limit on the ratio of gamma rays to cosmic rays of 1.2 x 10(-3) for the flux coming from the Galactic plane region (-80 degrees less than or similar to l less than or similar to -30 degrees; -10 degrees less than or similar to b less than or similar to 5 degrees) in the energy range 1.2-6.0 PeV. In the same energy range, point source fluxes with E-2 spectra have been excluded at a level of (E/TeV)(2)d Phi/dE similar to 10(-12)-10(-11) cm(-2) s(-1) TeV-1 depending on source declination. The complete IceCube detector will have a better sensitivity (due to the larger detector size), improved reconstruction, and vetoing techniques. Preliminary data from the nearly final IceCube detector configuration have been used to estimate the 5-yr sensitivity of the full detector. It is found to be more than an order of magnitude better, allowing the search for PeV extensions of known TeV gamma-ray emitters. DOI: 10.1103/PhysRevD.87.062002