The VINCY Cyclotron is the main part of the TESLA Accelerator Installation at the Vinča Institute of Nuclear Sciences in Belgrade. It is an isochroous cyclotron for the acceleration of both light and heavy ions. The pole of its magnet has the diameter of 2000 mm; its bending limit is 134 MeV, while its focusing limit is 73 MeV. This paper describes the magnetic field measurement system that has been used for the shimming of the VINCY Cyclotron magnet i.e., for precise shaping of its sectors and plugs. It is an automatic measurement system based on the Hall-probe that moves in the median plane between the poles of the magnet. We have used this system to obtain precise maps of the magnetic field for different operating regimes of the cyclotron needed in the process of shimming. The overall measurement uncertainty was estimated to be in the range of ±0.02%.