Barium (Ba) stars are chemically peculiar stars that display in their atmospheres signatures of the slow neutron-capture (s-process) mechanism that operates within asymptotic giant branch (AGB) stars, an important contributor to the cosmic abundance. The observed chemical peculiarity in these objects is not due to self-enrichment, but to mass transfer between the components of a binary system. The atmospheres of Ba stars are therefore excellent astrophysical laboratories, providing strong constraints for the nucleosynthesis of the s-process in AGB stars. In particular, rubidium (Rb) is a key element for the s-process diagnostic because it is sensitive to the neutron density and hence its abundance points to the main neutron source of the s-process in AGB stars. We present Rb abundances for a large sample of 180 Ba stars from high-resolution spectra (R = 48 000), and we compare the observed [Rb/Zr] ratios with theoretical predictions from s-process models in AGB stars. The target Ba stars in this study display [Rb/Zr] < 0, showing that Rb was not efficiently produced by the activation of the branching points at 85Kr and 86Rb. Model predictions from the Monash and FRUITY datasets of low-mass (≤4 MO) AGB stars are able to cover the Rb abundances observed in the program Ba stars. These observations indicate that the 13C(α,n)16O reaction is the main neutron source of the s-process in the low-mass AGB companions of the observed Ba stars. We have not found in the present study candidate companions for former IR/OH massive AGB stars.