The recent HEGRA observations of the blazar Mkn 501 show strong curvature in the very high energy \gamma -ray spectrum . Applying the \gamma -ray opacity derived from an empirically based model of the intergalactic infrared background radiation field ( IIRF ) , to these observations , we find that the intrinsic spectrum of this source is consistent with a power-law : { d } N _ { \gamma } / { d } E \propto E ^ { - \alpha } with \alpha = 2.00 \pm 0.03 over the range 500 GeV – 20 TeV . Within current synchrotron self-Compton scenarios , the fact that the TeV spectral energy distribution of Mkn 501 does not vary with luminosity , combined with the correlated , spectrally variable emission in X-rays , as observed by the BeppoSAX and RXTE instruments , also independently implies that the intrinsic spectrum must be close to \alpha = 2 . Thus , the observed curvature in the spectrum is most easily understood as resulting from intergalactic absorption .