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Observations of the GeV and TeV gamma-ray spectrum of the active galaxy Markarian 421 are used to derive an upper limit to the energy density of infra-red background radiation. This limit is derived through a consideration of high energy gamma-ray cascading in the presence of such radiation fields. The resulting upper bound proves to be the most restrictive for the wavelength range of 10-12 micrometers. These constraints are presently limited by the uncertainty of extrapolating the source spectrum from 5 to 500 GeV. Observations in the range 50-100 GeV would significantly improve these limits, allowing for a wide range of IR production models to be constrained.
