The TACTIC \gamma -ray telescope has observed Mrk 421 on 66 clear nights from Dec. 07 , 2005 to Apr . 30 , 2006 , totalling \sim 202 hours of on-source observations . Here , we report the detection of flaring activity from the source at \geq 1 TeV energy and the time-averaged differential \gamma -ray spectrum in the energy range 1 - 11 TeV for the data taken between Dec. 27 , 2005 to Feb. 07 , 2006 when the source was in a relatively higher state as compared to the rest of the observation period . Analysis of this data spell , comprising about \sim 97h reveals the presence of a \sim 12.0 \sigma \gamma -ray signal with daily flux of > 1 Crab unit on several days . A pure power law spectrum with exponent -3.11 \pm 0.11 as well as a power law spectrum with an exponential cutoff ( \Gamma = -2.51 \pm 0.26 and E _ { 0 } = ( 4.7 \pm 2.1 ) TeV ) are found to provide reasonable fits to the inferred differential spectrum within statistical uncertainties . We believe that the TeV light curve presented here , for nearly 5 months of extensive coverage , as well as the spectral information at \gamma -ray energies of > 5 TeV provide a useful input for other groups working in the field of \gamma -ray astronomy .