We propose an approach for estimating the permeability tensor using seismic emission induced by borehole hydraulic tests or by a fluid injection of an arbitrary nature. This approach provides a single estimation of the permeability tensor for the complete heterogeneous rock volume where the seismic emission was recorded. The approach is an extension of the method proposed by Shapiro et al. (1997) for the isotropic case. It is based on the hypothesis that the triggering front of the hydraulic-induced microseismicity propagates like a low-frequency second-type compressional Biot wave (corresponding to the process of pore-pressure relaxation) in an effective homogeneous anisotropic poroelastic fluid-saturated medium. The permeability tensor of this effective medium is the permeability tensor of the heterogeneous rock volume upscaled to the characteristic size of the seismically active region. We demonstrate the method using the microseismic data collected during the Hot Dry Rock Soultz-sous-Forêts experiment (Dyer et al. 1994). These data show that the corresponding rock volume is characterized by a significant permeability anisotropy caused by oriented crack systems. The maximal principal component of the permeability tensor has a subvertical orientation. It is about seven times larger than the minimal subhorizontal principal component.