The slow neutron capture process (s-process) is responsible for producing about half of the elemental abundances heavier than iron in the universe. Neutron capture cross sections on stable isotopes are a key nuclear physics input for s-process studies. The ⁷²Ge(n, γ) cross section has an important influence on production of isotopes between Ge and Zr during s-process in massive stars and therefore experimental data are urgently required. ⁷²Ge(n, γ) was measured at the neutron time-of-flight facility n_TOF (CERN) for the first time at stellar energies. The measurement was performed using an enriched ⁷²GeO₂ sample at a flight path of 185m with a set of liquid scintillation detectors (C₆D₆). The motivation, experiment and current status of the data analysis are reported.