Bunyaviruses are an emerging group of medically important viruses, many of which are transmitted from insects to mammals. To identify host factors that impact infection, we performed a genome-wide RNAi screen in Drosophila and identified 131 genes that impacted infection of the mosquito-transmitted bunyavirus Rift Valley fever virus (RVFV). Dcp2, the catalytic component of the mRNA decapping machinery, and two decapping activators, DDX6 and LSM7, were antiviral against disparate bunyaviruses in both insect cells and adult flies. Bunyaviruses 5′ cap their mRNAs by “cap-snatching” the 5′ ends of poorly defined host mRNAs. We found that RVFV cap-snatches the 5′ ends of Dcp2 targeted mRNAs, including cell cycle-related genes. Loss of Dcp2 allows increased viral transcription without impacting viral mRNA stability, while ectopic expression of Dcp2 impedes viral transcription. Furthermore, arresting cells in late S/early G2 led to increased Dcp2 mRNA targets and increased RVFV replication. Therefore, RVFV competes for the Dcp2-accessible mRNA pool, which is dynamically regulated and can present a bottleneck for viral replication.