Background: About 50% of heavy elements are produced by the slow neutron capture process (s process) in stars. The element gallium is mostly produced during the weak s process in massive stars. Purpose: Our activation at kBT≈25 keV is the first experiment in a series of activation and time-of-flight measurements on Ga69 and Ga71 relevant for astrophysics. Methods: We activated Ga69 and Ga71 with a neutron distribution that corresponds to a quasistellar distribution with kBT=25keV at the Joint Research Centre (JRC), Geel, Belgium. Protons were provided by an electrostatic Van de Graaff accelerator to produce neutrons via the reaction Li7(p,n). The produced activity was measured via the γ emission by the decaying product nuclei by high-purity germanium detectors. Results: We provide spectrum-averaged cross sections (SACS) and ratios of the cross sections σGa/σAu for the neutron spectrum of the activation. We obtain values of σ69Ga,SACS=(186±12)mb and σ71Ga,SACS=(112±7)mb, and cross-section ratios of σ69Ga/σAu=0.29±0.02 and σ71Ga/σAu=0.17±0.01. Conclusions: Our data disagree with the available evaluated data provided by KADoNiS v0.3, our cross-section ratio is about 20% higher for Ga69 and about 20% lower for Ga71.