Exceptionally strong and long lasting flaring activity of the blazar Markarian 421 (Mrk 421) occurred between January and March 2001. Based on the excellent signal-to-noise ratio of the data we derive the energy spectrum between 260 GeV - 17 TeV with unprecedented statistical precision. The spectrum is not well described by a simple power law even with a curvature term. Instead the data can be described by a power law with exponential cutoff: $rm {{dN}over{dE}} propto rm E^{-2.14 pm 0.03_{stat}} times e^{-E/E_{0}} m^{-2} s^{-1} TeV^{-1}$ with $rm E_{0} = 4.3 pm 0.3_{stat} TeV$. Mrk 421 is the second $gamma$-ray blazar that unambiguously exhibits an absorption-like feature in its spectral energy distribution at 3-6 TeV suggesting that this may be a universal phenomenon, possibly due to the extragalactic infra-red background radiation.