Optomechanical SiN nano-oscillators in high-finesse Fabry-Perot cavities can be used to investigate the interaction between mechanical and optical degree of freedom for ultra-sensitive metrology and fundamental quantum mechanical studies. In this paper, we present a nano-oscillator made of a high-stress round-shaped SiN membrane with an integrated on-chip 3-D acoustic shield properly designed to reduce mechanical losses. This oscillator works in the range of 200 kHz to 5 MHz and features a mechanical quality factor of Q ≃ 10 7 and a Q-frequency product in excess of 6.2 × 10 12 Hz at room temperature, fulfilling the minimum requirement for quantum ground-state cooling of the oscillator in an optomechanical cavity. The device is obtained by MEMS deep reactive-ion etching (DRIE) bulk micromachining with a two-side silicon processing on a silicon-on-insulator wafer. The microfabrication process is quite flexible such that additional layers could be deposited over the SiN membrane before the DRIE steps, if required for a sensing application. Therefore, such oscillator is a promising candidate for quantum sensing applications in the context of the emerging field of quantum technologies.