The discovery of Very High Energy (VHE; E > 100 GeV) γ-ray emission from 4C +21.35 (PKS 1222+216) by MAGIC on 2010 June 17, triggered by the high activity detected by the Fermi Large Area Telescope (LAT) in high energy (HE) γ-rays, poses intriguing questions on the location of the γ-ray emitting region in this flat spectrum radio quasar (FSRQ). We present multifrequency data of 4C +21.35 collected from radio to VHE during 2010 for investigating the properties of this source and discussing a possible emission model. The first hint of detection at VHE was observed by MAGIC on 2010 May 3, soon after a γ-ray flaring activity detected by Fermi-LAT and peaking on April 29. The same emission mechanism may therefore be responsible for both the HE and VHE emission during the 2010 flaring episodes. Two optical peaks were detected on 2010 April 20 and June 30, close in time but not simultaneous with the two γ-ray peaks, while no clear correlation was observed between the X-ray and γ-ray emission. An increasing flux density was observed in radio and mm bands from the beginning of 2009, in accordance with the increasing γ-ray activity observed by Fermi-LAT, and peaking on 2011 January 27 at 230 GHz. We model the spectral energy distributions (SEDs) of 4C +21.35 for the two periods of the VHE detection and a quiescent state with a one-zone model considering the emission from a very compact region outside the broad line region. The three SEDs could be fit with a combination of synchrotron self-Compton and external Compton emission of seed photons from a dust torus, changing only the electron distribution parameters among the SEDs. The fit of the optical/UV part of the spectrum for 2010 April 29 seems to favor an inner disk radius of 3 gravitational radii, a value expected for a maximally prograde rotating Kerr black hole.