Recent findings have highlighted an interconnection between intestinal microbiota and the brain, referred to as microbiota–gut–brain axis, and suggested that alterations in microbiota composition might affect brain functioning, also in Alzheimer’s disease. To investigate microbiota–gut–brain axis biochemical pathways, in this work we developed an innovative device to be used as modular unit in an engineered multi-organ-on-a-chip platform recapitulating in vitro the main players of the microbiota–gut–brain axis, and an innovative three-dimensional model of brain cells based on collagen/hyaluronic acid or collagen/poly(ethylene glycol) semi-interpenetrating polymer networks and β-amyloid precursor protein-Swedish mutant-expressing H4 cells, to simulate the pathological scenario of Alzheimer’s disease. We set up the culturing conditions, assessed cell response, scaled down the three-dimensional models to be hosted in the organ-on-a-chip device, and cultured them both in static and in dynamic conditions. The results suggest that the device and three-dimensional models are exploitable for advanced engineered models representing brain features also in Alzheimer’s disease scenario.