Very high energy ( VHE ) \gamma -ray emission from the flat spectrum radio quasar ( FSRQ ) PKS 1222+21 ( 4C 21.35 , z =0.432 ) was detected with the MAGIC Cherenkov telescopes during a short observation ( \sim 0.5 hr ) performed on 2010 June 17 . The MAGIC detection coincides with high energy MeV/GeV \gamma -ray activity measured by the Large Area Telescope ( LAT ) on board the Fermi satellite . The VHE spectrum measured by MAGIC extends from about 70 GeV up to at least 400 GeV and can be well described by a power law d { N } / d { E } \propto { E } ^ { - \Gamma } with a photon index \Gamma = 3.75 \pm 0.27 _ { \tiny \mbox { stat } } \pm 0.2 _ { \tiny \mbox { syst } } . The averaged integral flux above 100 GeV is ( 4.6 \pm 0.5 ) \times 10 ^ { -10 } \mbox { cm } ^ { -2 } \mbox { s } ^ { -1 } ( \sim 1 Crab Nebula flux ) . The VHE flux measured by MAGIC varies significantly within the 30 minutes exposure implying a flux doubling time of about 10 minutes . The VHE and MeV/GeV spectra , corrected for the absorption by the extragalactic background light ( EBL ) , can be described by a single power law with photon index 2.72 \pm 0.34 between 3 GeV and 400 GeV , and is consistent with emission belonging to a single component in the jet . The absence of a spectral cutoff constrains the \gamma -ray emission region to lie outside the broad-line region , which would otherwise absorb the VHE \gamma -rays . Together with the detected fast variability , this challenges present emission models from jets in FSRQs . Moreover , the combined Fermi /LAT and MAGIC spectral data yield constraints on the density of the EBL in the UV-optical to near-infrared range that are compatible with recent models .