In many Proteobacterial species, transcription and RNA degradation are physically separated through segregation of the main ribonucleolytic machinery—the RNA degradosome—into RNase E-driven membrane-anchored assemblies that form discrete foci. Despite widespread conservation of the amphipathic membrane-targeting sequence (MTS) in RNase E, its function and biological importance remain poorly understood. Here, we have investigated how the MTS contributes to bacterial virulence or stress response in Pseudomonas aeruginosa. We show that membrane anchoring is dispensable for formation of RNA degradosome foci, but required for their proper morphology, dynamics, and localization, whereas the MTS sequence modulates foci behavior. Transcriptomic and mRNA spatial organization analyses further reveal specific stabilization of localized transcripts encoding membrane proteins in the MTS mutant, together with abnormal operon processing. Altogether, our study reveals the elegant MTS-mediated control of RNA degradosome spatial organization and target selection, shaping the transcriptome and bacterial stress responses.