Hexagonal group IV materials like silicon and germanium are expected to display remarkable optoelectronic properties for future development of photonic technologies. However, the fabrication of hexagonal group IV semiconductors within the vapour-liquid-solid method has been obtained using gold as a catalyst thus far. In this letter, we show the synthesis of hexagonal Ge on self-assisted GaAs nanowires using molecular beam epitaxy. With an accurate tuning of the Ga and As molecular beam flux we selected the crystal phase, cubic or hexagonal, of the GaAs NWs during the growth. A 500 nm-long hexagonal segment of Ge with high structural quality and without any visible defects is obtained, and we show that germanium keeps the crystal phase of the core using scanning transmission electron microscopy. Finally X-ray Photoelectron Spectroscopy reveals a strong incorporation of As in the Ge. This study demonstrates the first growth of hexagonal Ge in the Au-free approach, integrated on silicon substrate.