Abstract : Aims: We investigate the peculiar properties of a large TeV γ-ray flare from Mrk 501 detected during the 2009 multiwavelength campaign. Methods: We identified the counterpart of the flare in the Fermi/LAT telescope data and studied its spectral and timing characteristics. Results: A strong order-of-magnitude increase of the very-high-energy γ-ray flux during the flare was not accompanied by an increase in the X-ray flux, so that the flare was one of the "orphan"-type TeV flares observed in BL Lacs. The flare lasted about one month at energies above 10 GeV. The flaring source spectrum in the 10-200 GeV range was very hard, with a photon index Γ = 1.1 ± 0.2, harder than that observed in any other blazar in the γ-ray band. No simultaneous flaring activity was detected below 10 GeV. Different variability properties of the emission below and above 10 GeV indicate the existence of two separate components in the spectrum. We investigate possible explanations of the very hard flaring component. We consider, among others, the possibility that the flare is produced by an electromagnetic cascade initiated by very-high-energy γ-rays in the intergalactic medium. Within such an interpretation, peculiar spectral and temporal characteristics of the flare could be explained if the magnetic field in the intergalactic medium is on the order of 10-17 - 10-16 G.