An extraordinary flare from blazar Mrk 421 was recorded on the night of April 24, 2014, by the Major Atmospheric Gamma Imaging Cherenkov (MAGIC) telescopes at very high energy (VHE) from 100 GeV up to 10 TeV. Several quantum-gravity models indicate that the photon group velocity in vacuum may be energy dependent, known as in-vacuum dispersion. Violation of Lorentz Invariance (LIV) of this kind can lead to an observable effect on the time of flight of VHE photons from cosmic origin. Observations of fast and distant phenomena, such as the flare from Mrk 421, are excellent testing grounds for this hypothesis. Using an innovative binned likelihood analysis, for the first time from this source we were able to search for arrival-time delays scaling linearly or quadratically with the energy of the photon. The non-detection of energy-dependent time delays led us to set constraints on the parameter space of quantum-gravity predictions.