We have 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 $sqrt{s_{_{NN}}}=200$ GeV. The $e^{+}e^{-}$ contribution from quasi-real 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$pm$53(stat)$pm$57(syst)~MeV/$c$ and 333$pm$72(stat)$pm$45(syst)~MeV/$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 $dN_{rm ch}/deta$ observed in Au$+$Au at the same collision energy.
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