  We report the first observation of $B_s^0\to J/\psi\eta$ and evidence for
$B_s^0\to J/\psi\eta'$. These results are obtained from $23.6 \mathrm{fb}^{-1}$
of data collected at the $\Upsilon(5S)$ resonance with the Belle detector at
the KEKB $e^+e^-$ collider. We measure the branching fractions
$\mathcal{B}(B_s^0\to J/\psi\eta)= (3.32 \pm
0.87(\mathrm{stat.})^{+0.32}_{-0.28}(\mathrm{syst.}) \pm 0.42(f_s))\times
10^{-4}}$ with a significance of $7.3 \sigma$, and $\mathcal{B}(B_s^0\to
J/\psi\eta')= (3.1 \pm 1.2(\mathrm{stat.})^{+0.5}_{-0.6}(\mathrm{syst.}) \pm
0.38(f_s))\times 10^{-4}$ with a significance of $3.8 \sigma$.
