The first measurements of the differential cross section for the d(γ,p)n reaction up to 4.0 GeV were performed at the Continuous Electron Beam Accelerator Facility (CEBAF) at Thomas Jefferson Laboratory. We report the cross sections at the proton center-of-mass angles of 36°, 52°, 69°, and 89°. These results are in reasonable agreement with previous measurements at lower energy. The 89° and 69° data show constituent-counting-rule behavior up to 4.0 GeV photon energy. The 52° and 36° data disagree with the counting-rule behavior. The quantum chromodynamics (QCD) model of nuclear reactions involving reduced amplitudes disagrees with the present data.