The recent High-Energy Gamma-Ray Array (HEGRA) observations of the blazar M
rk 501 show strong curvature in the very high energy gamma-ray spectrum. Ap
plying the gamma-ray opacity derived from an empirically based model of the
intergalactic infrared background radiation field to these observations, w
e find that the intrinsic spectrum of this source is consistent with a powe
r law: dN(gamma)/dE proportional to E-alpha, with alpha = 2.00 +/- 0.03 ove
r the range 500 GeV-20 TeV. Within current synchrotron self-Compton scenari
os, the fact that the TeV spectral energy distribution of Mrk 501 does not
vary with luminosity, combined with the correlated, spectrally variable emi
ssion in X-rays as observed by the BeppoSAX and Rossi X-Ray Timing Explorer
instruments, also independently implies that the intrinsic spectrum must b
e close to alpha = 2. Thus, the observed curvature in the spectrum is most
easily understood as resulting from intergalactic absorption.