Protocells containing enzyme-driven biomolecular circuits that can process and exchange information offer a promising approach for mimicking cellular features and developing molecular information platforms. Here, we employ synthetic transcriptional circuits together with CRISPR/Cas-based DNA processing inside semipermeable protein-polymer microcompartments. We first establish a transcriptional protocell that can be activated by external DNA strands and produce functional RNA aptamers. Subsequently, we engineer a transcriptional module to generate RNA strands functioning as diffusive signals that can be sensed by neighboring protocells and trigger the activation of internalized DNA probes or localization of Cas nucleases. Our results highlight the opportunities to combine CRISPR/Cas machinery and DNA nanotechnology for protocellular communication and provide a step towards the development of protocells capable of distributed molecular information processing.