Aims: We investigate the extension of the very high-energy spectral tail of the Crab Pulsar at energies above 400 GeV. Methods: We analyzed ~320 h of good-quality Crab data obtained with the MAGIC telescope from February 2007 to April 2014. Results: We report the most energetic pulsed emission ever detected from the Crab Pulsar reaching up to 1.5 TeV. The pulse profile shows two narrow peaks synchronized with those measured in the GeV energy range. The spectra of the two peaks follow two different power-law functions from 70 GeV up to 1.5 TeV and connect smoothly with the spectra measured above 10 GeV by the Large Area Telescope (LAT) on board the Fermi satellite. When making a joint fit of the LAT and MAGIC data above 10 GeV the photon indices of the spectra differ by 0.5 ± 0.1. Conclusions: Using data from the MAGIC telescopes we measured the most energetic pulsed photons from a pulsar to date. Such TeV pulsed photons require a parent population of electrons with a Lorentz factor of at least 5 × 106. These results strongly suggest IC scattering off low-energy photons as the emission mechanism and a gamma-ray production region in the vicinity of the light cylinder.