  The doubly-magic nucleus $^{16}$O has a small neutron capture cross section
of just a few tens of microbarn in the astrophysical energy region. Despite of
this, $^{16}$O plays an important role as neutron poison in the astrophysical
slow neutron capture ($s$) process due to its high abundance. We present in
this paper a re-evaluation of the available experimental data for
$^{16}$O($n,\gamma$)$^{17}$O and derive a new recommendation for the
Maxwellian-averaged cross sections (MACS) between $kT$= 5$-$100 keV. Our new
recommendations are lower up to $kT$= 60 keV compared to the previously
recommended values but up to 14\% higher at $kT$= 100 keV. We explore the
impact of this different energy dependence on the weak $s$-process during core
helium- ($kT$= 26 keV) and shell carbon burning ($kT$= 90 keV) in massive stars
where $^{16}$O is the most abundant isotope.
