We report on the conversion to telecommunication wavelengths of single photons emitted by a nitrogen-vacancy (NV) defect in diamond. By means of difference frequency generation, we convert spin-selective photons at 637 nm, associated with the coherent NV zero-phonon line, to the target wavelength of 1588 nm in the L-telecommunication band. The successful conversion is evidenced by time-resolved detection revealing a telecommunication-photon lifetime identical to that of the original 637-nm photon. Furthermore, we show by second-order correlation measurements that the single-photon statistics are preserved. The overall efficiency of this one-step conversion reaches 17% in our current setup, along with a signal-to-noise ratio of approximately 7 despite the low probability (<10-3) of an incident 637-nm photon. This result shows the potential for efficient telecommunication-photon-NV-center interfaces and marks an important step towards future long-range entanglement-based quantum networks.