^{140}Ce(n,γ) is a key reaction for slow neutron-capture (s-process) nucleosynthesis due to being a bottleneck in the reaction flow. For this reason, it was measured with high accuracy (uncertainty ≈5%) at the n_TOF facility, with an unprecedented combination of a high purity sample and low neutron-sensitivity detectors. The measured Maxwellian averaged cross section is up to 40% higher than previously accepted values. Stellar model calculations indicate a reduction around 20% of the s-process contribution to the Galactic cerium abundance and smaller sizeable differences for most of the heavier elements. No variations are found in the nucleosynthesis from massive stars.