We use the new results of the HEGRA detector on the TeV gamma-ray emission from MKN 501 to set upper limits on the energy density of the cosmic infrared background (CIRB). Contrary to previous interpretations of the gamma-ray spectrum of MKN 421 as showing an intergalactic absorption cutoff at 5 TeV, the observed spectrum of MKN 501 extends beyond 10 TeV and appears to be unattenuated by gamma-gamma collisions with the low-energy CIRB photons. The upper limits on the CIRB intensity -- derived both assuming an `a priori' shape for the CIRB spectrum and without model-dependent assumptions -- are thus quite strong and come almost in conflict with the observational evaluations based on deep surveys of extragalactic sources in the near- and mid-IR. If spectra at TeV energies for extragalactic gamma-ray sources like this for MKN 501 will be confirmed with improved statistics, we may be forced to conclude that the process of gamma-gamma interaction in the intergalactic space is more complex than expected and the average intergalactic magnetic field extremely weak.