A search for the $Bs0\to D\ast \pm D\mp$ decay is performed using proton-proton collision data at centre-of-mass energies of $7$, $8$ and $13TeV$ collected by the LHCb experiment, corresponding to an integrated luminosity of $9fb-1$. The decay is observed with a high significance and its branching fraction relative to the $B0\to D\ast \pm D\mp$ decay is measured to be \begin{align*} \frac{\mathcal{B}(B_s^0 \rightarrow D^{\ast \pm} D^{\mp}) }{\mathcal{B}(B^0 \rightarrow D^{\ast \pm} D^{\mp}) } = 0.137 \pm 0.017 \pm 0.002 \pm 0.006 ,, \end{align*} where the first uncertainty is statistical, the second systematic and the third is due to the uncertainty on the ratio of the $Bs0$ and $B0$ hadronisation fractions.