The KM3NeT collaboration operates two water Cherenkov neutrino telescopes in the Mediterranean sea, ORCA and ARCA. The flux of atmospheric muons produced in cosmic ray air showers forms a background to the main objectives of KM3NeT/ORCA and KM3NeT/ARCA, respectively measuring atmospheric neutrino oscillations and detecting neutrinos from astrophysical sources. A small portion of the atmospheric muons stops inside the detector’s instrumented volume. The stopping muons are 5% of the muons reconstructed using the 6 first strings deployed for ORCA. This still amounts to 1000 events per hour. We present two methods for selecting them, applied on both simulations and data. The first method uses simple cuts on a set of reconstructed variables. The second method uses a machine learning model to classify muons as “stopping” or “crossing”. Both methods allow to reach a high selection purity, close to 95%. Detecting stopping muons can serve many purposes like studying muon decay via the detection of Michel electrons or estimating the flux of atmospheric muons at sea level. This work highlights the accurate reconstruction capabilities of ORCA. The median error on the reconstructed stopping point of selected muons is less than 5 meters, and the median angular deviation is 1° . This is to be compared with the 20 meters horizontal distance between strings and the 9 meters vertical distance between optical modules. Another important result is the excellent agreement between distribution of stopping muons selected in data and in simulations.}