The neurovascular unit, which consists of vascular cells surrounded by astrocytic end-feet and neurons, controls cerebral blood flow and the permeability of the blood–brain barrier (BBB) to maintain homeostasis in the neuronal milieu. Studying how some pathogens and drugs can penetrate the human BBB and disrupt neuronal homeostasis requires in vitro microphysiological models of the neurovascular unit. Here we show that the neurotropism of Cryptococcus neoformans—the most common pathogen causing fungal meningitis—and its ability to penetrate the BBB can be modelled by the co-culture of human neural stem cells, brain microvascular endothelial cells and brain vascular pericytes in a human-neurovascular-unit-on-a-chip maintained by a stepwise gravity-driven unidirectional flow and recapitulating the structural and functional features of the BBB. We found that the pathogen forms clusters of cells that penetrate the BBB without altering tight junctions, suggesting a transcytosis-mediated mechanism. The neurovascular-unit-on-a-chip may facilitate the study of the mechanisms of brain infection by pathogens, and the development of drugs for a range of brain diseases.