In this letter, we address parametric channel estimation in a multi-user multiple-input multiple-output system within the radiative near-field of the base station array with aperture antennas. We investigate a two-dimensional multiple signal classification algorithm (2D-MUSIC) to estimate both the range and the azimuth angles of arrival for the users' channels, utilizing parametric radiative near-field channel models. We analyze the performance of the algorithm by deriving the Cram & eacute;r-Rao bound (CRB) for parametric estimation, and its effectiveness is compared against the least squares estimator, which is a non-parametric estimator. Numerical results indicate that the 2D-MUSIC algorithm outperforms the least squares estimator. Furthermore, the results demonstrate that the performance of 2D-MUSIC achieves the parametric channel estimation CRB, which shows that the algorithm is asymptotically consistent.