The $^{63}$Ni($n, \gamma$) cross section has been measured for the first time at the neutron time-of-flight facility n\_TOF at CERN from thermal neutron energies up to 200 keV. In total, capture kernels of 12 (new) resonances were determined. Maxwellian Averaged Cross Sections were calculated for thermal energies from kT = 5 keV to 100 keV with uncertainties around 20%. Stellar model calculations for a 25 M$_\odot$ star show that the new data have a significant effect on the $s$-process production of $^{63}$Cu, $^{64}$Ni, and $^{64}$Zn in massive stars, allowing stronger constraints on the Cu yields from explosive nucleosynthesis in the subsequent supernova.
