Located in a dense complex environment, W51C provides an excellent scenario to probe accelerated protons in SNRs and their interaction with surrounding target material. Here we report the observation of extended Very High Energy (VHE) gamma-ray emission from the W51C supernova remnant (SNR) with MAGIC. Detections of extended gamma-ray emission in the same region have already been reported by the Fermi and H.E.S.S. collaborations. Fermi/LAT measured the source spectrum in the energy range between 0.2 and 50 GeV, which was found to be well fit by a hadronic neutral-pion decay model. The VHE observations presented here, obtained with the improved MAGIC stereo system, allow us to pinpoint the VHE gamma-ray emission in the dense shocked molecular cloud surrounding the remnant shell. The MAGIC data also allow us to measure, for the first time, the VHE emission spectrum of W51C from the highest Fermi/LAT energies up to TeV. The spatial distribution and spectral properties of the VHE emission suggest a hadronic origin of the observed gamma rays. Therefore W51C is a prime candidate for a cosmic ray accelerator.