The Rift Valley fever virus (RVFV) is the causative agent of fatal hemorrhagic fever in humans and acute hepatitis in ruminants. We found that infection by RVFV leads to a rapid and drastic suppression of host cellular RNA synthesis that parallels a decrease of the TFIIH transcription factor cellular concentration. Using yeast two hybrid system, recombinant technology, and confocal microscopy, we further demonstrated that the nonstructural viral NSs protein interacts with the p44 component of TFIIH to form nuclear filamentous structures that also contain XPB subunit of TFIIH. By competing with XPD, the natural partner of p44 within TFIIH, and sequestering p44 and XPB subunits, NSs prevents the assembly of TFIIH subunits, thus destabilizing the normal host cell life. These observations shed light on the mechanism utilized by RVFV to evade the host response.