A precise measurement of the cosmic-ray proton spectrum is carried out with the Calorimetric Electron Telescope (CALET) and a sharp softening of the energy spectrum above 10 TeV is observed. CALET, located on the International Space Station, has started data taking in October 2015 and has accumulated data for more than seven years without any serious troubles. CALET is pursuing the direct measurement of the main components of high energy cosmic rays up to ~1 PeV in order to understand the cosmic ray acceleration and propagation. Thanks to the thick calorimeter that corresponds to 30 radiation lengths and to \sim1.3 proton interaction lengths, the proton analysis presented in this paper spans a broad energy range from 50 GeV to 60 TeV. Proton energy resolution is 30-40%, and the residual background is less than 10% in the E < 10 TeV region. In the multi-TeV region, we observed a spectral softening with a spectral index change from -2.6 to -2.9 in addition to the spectral hardening we had previously confirmed with a high significance above a few hundred GeV. The transition to the softer regime is much sharper than the smooth onset of hardening observed at lower energy.