Recently observed minute-time-scale variability of blazar emission at TeV energies has imposed severe constraints on jet models and TeV emission mechanisms. We focus on a robust jet instability to explain this variability. As a consequence of the bulk outflow of the jet plasma, the pressure is likely to be anisotropic, with the parallel pressure P|| in the forward jet direction exceeding the perpendicular pressure P⊥. Under these circumstances, the jet is susceptible to the firehose instability, which can cause disruptions in the large-scale jet structure and result in variability of the observed radiation. For a realistic range of parameters, we find that the growth time-scale of the firehose instability is ≈ a few minutes, in good agreement with the observed TeV variability time-scales for Mrk 501 and PKS 2155−304.