Inhibition plays an important role in controlling the flow and processing of auditory information throughout the central auditory pathway, yet how inhibition shapes auditory processing in the medial geniculate body (MGB), the key region in the auditory thalamus, is poorly understood. MGB gates the flow of auditory information to the auditory cortex, and it is inhibited largely by the thalamic reticular nucleus (TRN). The TRN comprises two major classes of inhibitory neurons: parvalbumin (PVTRN)-positive and somatostatin (SSTTRN)-positive neurons. PV and SST neurons have been shown to play differential roles in controlling sound responses in other brain regions. In the somatosensory and visual subregions of the TRN, PVTRN and SSTTRN neurons exhibit anatomical and functional differences. However, it remains unknown whether and how PVTRN and SSTTRN neurons differ in their anatomical projections from the TRN, and whether and how they differentially modulate activity in the MGB. We find that PVTRN and SSTTRN neurons exhibit differential projection patterns within the thalamus: PVTRN neurons predominantly project to ventral MGB, whereas SSTTRN neurons project to the dorso-medial regions of MGB. Furthermore, PVTRN and SSTTRN neurons bi-directionally modulate sound responses in MGB. Selective optogenetic inactivation of PVTRN neurons increased sound-evoked activity in over a third of MGB neurons, while another large fraction of neurons showed suppressed activity. In contrast, inactivating SSTTRN neurons largely reduced tone-evoked activity in MGB neurons. Cell type-specific computational models identified candidate circuit mechanisms for generating the bi-directional effects of TRN inactivation on MGB sound responses. These distinct inhibitory pathways within the auditory thalamus reveal a cell type-specific role for thalamic inhibition in auditory computation.