We measured direct photons for p(T) < 5 GeV/c in minimum bias and 0%-40% most-central events at midrapidity for Cu+Cu collisions at root S-NN = 200 GeV. The e(+)e(-) contribution from quasireal direct virtual photons has been determined as an excess over the known hadronic contributions in the e(+)e(-) mass distribution. A clear enhancement of photons over the binary scaled p+p fit is observed for p(T) < 4 GeV/c in Cu+Cu data. The p(T) spectra are consistent with the Au+Au data covering a similar number of participants. The inverse slopes of the exponential fits to the excess after subtraction of the p+p baseline are 285 +/- 53 (stat) +/- 57(syst) MeV/c and 333 +/- 72(stat) +/- 45(syst) MeV/c for minimum bias and 0%-40% most-central events, respectively. The rapidity density, dN / dy, of photons demonstrates the same power law as a function of dN(ch)/d eta observed in Au+Au at the same collision energy.