Ultra-small (about 10 nm), low-strain, artificially produced diamonds with an internal, active color center have substantial potential for quantum information processing and biomedical applications.Thus, it is of great importance to be able to artificially produce such diamonds. Here, we report on the high-pressure, high-temperature synthesis of such nanodiamonds about 10 nm in size and containing an optically active, single silicon-vacancy color center. Using special sample preparation technique, we were able to prepare samples containing single nanodiamonds on the surface. By correlating atomic-force microscope images and confocal optical images we verified presents of optically active color centers in single nanocrystals, and using second-order correlation measurements proved single-photon emission statistics of this nanodiamonds. This color centers have non-blinking, spectrally narrow emission with narrow distribution of spectral width and positions of zero-phonon line thus proving high quality of the nanodiamonds produced.