Recently, the AGILEγ-ray telescope has reported enhanced γ-ray emission above 100 MeV from the direction of the Crab nebula during a period of a few days. This intriguing observation has been confirmed by the Fermi Large Area Telescope (LAT). This emission does not show evidence of pulsations with the Crab pulsar. It seems that it originates at the shock region created as a result of the interaction of the pulsar wind with the nebula. We propose that such variable γ-ray emission originates in the region behind the shock when the electrons can be accelerated as a result of the reconnection of the magnetic field compressed by the decelerating pulsar wind. The natural consequence of such an interpretation is the prediction that the Crab nebula γ-ray spectrum produced by electrons, as a result of the inverse Compton (IC) scattering of soft radiation to multi-TeV energies, should also show synchronous variability on the time-scales as observed at GeV energies by AGILE and Fermi-LAT. We calculate how the end of the IC component of the Crab nebula γ-ray spectrum should look during the quiescent and the flare GeV γ-ray emission. We conclude that the variability of the multi-TeV γ-ray spectrum from the Crab nebula might, in principle, be responsible for the differences between the spectral features reported by the High-Energy Gamma-Ray Astronomy (HEGRA) and High-Energy Stereoscopic System (HESS) collaborations at multi-TeV energies.