Exceptionally strong and long-lasting flaring activity of the blazar Mrk 421 occurred between 2001 January and March. Based on the excellent signal-to-noise ratio of the data, we derive the energy spectrum between 260 GeV and 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: with TeV. Mrk 421 is the second g-ray blazar thatunambiguously exhibits an absorption-like feature in its spectral energy distribution at 3-6 TeV. Subject headings: BL Lacertae objects: individual (Markarian 421) -gamma rays: observationsSince the discovery of TeV g-rays from BL Lac objects Mrk 421 (Punch et al. 1992) and Mrk 501 (Quinn et al. 1996), detailed very high energy observations of these nearby blazars (z p , ) have been made. Measurements of flux var-0.031 z p 0.034 iation with time, particularly simultaneous measurements at several wavelengths, constrain models of particle acceleration and g-ray production in the jets. Spectral energy density measurements constrain both the models of the jets and of the infrared photon density in the intervening intergalactic medium. The possibility of absorption of g-rays by IR radiation has been predicted for some time (Nikishov 1962;Gould & Schrèder 1967;Stecker, De Jager, & Salamon 1992), and implications of recent observations have been discussed (see, e.g., Biller et al. 1998;Stanev & Franceschini 1998;Vassiliev 1999).The general picture that has emerged for the spectral energy density of emitted radiation from BL Lac objects has two components: a lower one with energies extended up to about