The Josephson junction (JJ) is the corner stone of superconducting electronics and quantum information processing. While the technology for fabricating low Tc JJ is mature and delivers quantum circuits able to reach the "quantum supremacy", the fabrication of reproducible and low-noise high-Tc JJ is still a challenge to be taken up. Here we report on noise properties at RF frequencies of recently introduced high-Tc Josephson nano-junctions fabricated by mean of a Helium ion beam focused at sub-nanometer scale on a YBa2Cu3O7 thin film. We show that their current-voltage characteristics follow the standard Resistively-Shunted-Junction (RSJ) circuit model, and that their characteristic frequency fc = (2e/h)IcRn reaches ~300 GHz at low temperature. Using the "detector response" method, we evidence that the Josephson oscillation linewidth is only limited by the thermal noise in the RSJ model for temperature ranging from T ~ 20 K to 75 K. At lower temperature and for the highest He irradiation dose, the shot noise contribution must also be taken into account when approaching the tunneling regime. We conclude that these Josephson nano-junctions present the lowest noise level possible, which makes them very promising for future applications in the microwave and terahertz regimes.