It was recently proposed that a giant flare of the blazar PKS B1424-418 at redshift z = 1.522 is in association with a PeV-energy neutrino event detected by IceCube. Based on this association we here suggest that the flight time difference between the PeV neutrino and gamma-ray photons from blazar flares can be used to constrain the violations of equivalence principle (EP) and the Lorentz invariance for neutrinos. From the calculated Shapiro delay due to clusters or superclusters in the nearby universe, we find that violation of the equivalence principle for neutrinos and photons is constrained to an accuracy of at least 10 −5 , which is two orders of magnitude tighter than the constraint placed by MeV neutrinos from supernova 1987A. Lorentz invariance violation (LIV) arises in various quantum-gravity theories, which predicts an energy-dependent velocity of propagation in vacuum for photons and neutrinos. We find that the association of the PeV neutrino with the gamma-ray outburst set limits on the energy scale of possible LIV to > 0.01E pl for linear LIV models and > 6 × 10 −8 E pl for quadratic order LIV models, where E pl is the Planck energy scale. These are the most stringent constraints on neutrino LIV for subluminal neutrinos. −262 TeV and a median positional uncertainty of R 50 = 15.9 • centered at the coordinate RA=208.4 • , Dec=−55.8 • (J2000). By searching this field for positional coincidences with gamma-ray-emitting active galactic nuclei (AGNs), a high-fluence outburst of the blazar PKS B1424-418 is found to be in temporal and positional coincidence with the neutrino event [3]. An association between the giant flare of PKS B1424-418 and the PeV neutrino is then suggested based on the unprecedented nature of the two events and a posteriori probability for chance coincidence of about 5% (i.e. a 2 σ confidence correlation) [3]. It is also argued that the flare provides an energy output high enough to explain the observed PeV event [3]. PKS B1424-418 is at redshift z = 1.522 and classified as a flat spectrum radio quasar [5].