  As is well known, the smallest neutrino mass turns out to be vanishing in the
minimal seesaw model, since the effective neutrino mass matrix $M^{}_\nu$ is of
rank two due to the fact that only two heavy Majorana neutrinos are introduced.
In this paper, we point out that the one-loop matching condition for the
effective dimension-five neutrino mass operator can make an important
contribution to the smallest neutrino mass. By using the available one-loop
matching condition and two-loop renormalization group equations in the
supersymmetric version of the minimal seesaw model, we explicitly calculate the
smallest neutrino mass in the case of normal neutrino mass ordering and obtain
$m^{}_1 \approx 6.7\times 10^{-10}~{\rm eV}$ at the Fermi scale
$\Lambda^{}_{\rm F} = 91.2~{\rm GeV}$ with some typical input at the seesaw
scale $\Lambda^{}_{\rm SS} = 10^{14}~{\rm GeV}$.
