RNA degradation is crucial for regulating gene expression in all organisms. Like the decapping of eukaryotic mRNAs, the conversion of the 5′-Terminal triphosphate of bacterial transcripts to a monophosphate can trigger RNA decay by exposing the transcript to attack by 5′-monophosphate-dependent ribonucleases. In both biological realms, this deprotection step is catalyzed by members of the Nudix hydrolase family. The genome of the gastric pathogen Helicobacter pylori, a Gramnegative epsilonproteobacterium, encodes two proteins resembling Nudix enzymes. Here we present evidence that one of them, HP1228 (renamed HpRppH), is an RNA pyrophosphohydrolase that triggers RNA degradation in H. pylori, whereas the other, HP0507, lacks such activity. In vitro, HpRppH converts RNA 5′-Triphosphates and diphosphates to monophosphates. It requires at least two unpaired nucleotides at the 5′ end of its substrates and prefers three or more but has only modest sequence preferences. The influence of HpRppH on RNA degradation in vivo was examined by using RNA-seq to search the H. pylori transcriptome for RNAs whose 5′-phosphorylation state and cellular concentration are governed by this enzyme. Analysis of cDNA libraries specific for transcripts bearing a 5′-Triphosphate and/or monophosphate revealed at least 63 potential HpRppH targets. These included mRNAs and sRNAs, several of which were validated individually by half-life measurements and quantification of their 5′-Terminal phosphorylation state in wild-Type and mutant cells. These findings demonstrate an important role for RppH in post-Transcriptional gene regulation in pathogenic Epsilonproteobacteria and suggest a possible basis for the phenotypes of H. pylori mutants lacking this enzyme.