Misfit-strain guided growth of periodic quantum dot (QD) arrays in planar thin film epitaxy has been a popular nanostructure fabrication method. Engineering misfit-guided QD growth on a nanoscale substrate such as the small curvature surface of a nanowire represents a new approach to self-organized nanostructure preparation. Perhaps more profoundly, the periodic stress underlying each QD and the resulting modulation of electro-optical properties inside the nanowire backbone promise to provide a new platform for novel mechano-electronic, thermoelectronic, and optoelectronic devices. Herein, we report a first experimental demonstration of self-organized and self-limited growth of coherent, periodic Ge QDs on a one-dimensional Si nanowire substrate. Systematic characterizations reveal several distinctively different modes of Ge QD ordering on the Si nanowire substrate depending on the core diameter. In particular, Ge QD arrays on Si nanowires of around 20 nm diameter predominantly exhibit an anticorrelated pattern whose wavelength agrees with theoretical predictions. The correlated pattern can be attributed to propagation and correlation of misfit strain across the diameter of the thin nanowire substrate. The QD array growth is self-limited as the wavelength of the QDs remains unchanged even after prolonged Ge deposition. Furthermore, we demonstrate a direct kinetic transformation from a uniform Ge shell layer to discrete QD arrays by a postgrowth annealing process.