The design and construction of synthetic prototissues from integrated assemblies of artificial protocells is an important challenge for synthetic biology and bioengineering. Here we spatially segregate chemically communicating populations of enzyme-decorated phospholipid-enveloped polymer/DNA coacervate protocells in hydrogel modules to construct a tubular prototissue-like vessel capable of modulating the output of bioactive nitric oxide (NO). By decorating the protocells with glucose oxidase, horseradish peroxidase or catalase and arranging different modules concentrically, a glucose/hydroxyurea dual input leads to logic-gate signal processing under reaction-diffusion conditions, which results in a distinct NO output in the internal lumen of the model prototissue. The NO output is exploited to inhibit platelet activation and blood clot formation in samples of plasma and whole blood located in the internal channel of the device, thereby demonstrating proof-of-concept use of the prototissue-like vessel for anticoagulation applications. Our results highlight opportunities for the development of spatially organized synthetic prototissue modules from assemblages of artificial protocells and provide a step towards the organization of biochemical processes in integrated micro-compartmentalized media, micro-reactor technology and soft functional materials.