Particle aggregates are frequently encountered in many natural and industrial environments. We describe here the stationary state of the fragmentation process of inertial scale particle aggregates in turbulence, i.e., when the particles and the aggregates are larger than the Kolmogorov dissipative scale η. For this purpose, we place at the initial time a large aggregate of millimetric, nearly neutrally buoyant magnetic particles in a high-Reynolds-number turbulent von Kármán flow. Turbulent fluctuations impose external stresses that tend to fragment the initial and the subsequent aggregates, contrary to the magnetic dipoles that impose torques and forces on the magnets responsible for cohesion. Using video image analyses, we perform the three-dimensional reconstruction of the aggregates and measure their characteristic sizes. The average number of particles inside each aggregate can then be deduced as a function of the intensity of turbulence. Assuming a Kolmogorov inertial scaling law for the turbulent velocity increments, we predict theoretically an aggregate mean size which is in agreement with our experimental results.