The shape of the $B_s^0rightarrow D_s^{*-}mu^+ u_{mu}$ differential decay rate is obtained as a function of the hadron recoil using proton-proton collision data at a centre-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 1.7 fb$^{-1}$ collected by the LHCb detector. The $B_s^0rightarrow D_s^{*-}mu^+ u_{mu}$ decay is reconstructed through the decays $D_s^{*-}rightarrow D_s^{-}gamma$ and $D_s^{-}rightarrow K^-K^+pi^-$. The differential decay rate is fitted with the Caprini-Lellouch-Neubert (CLN) and Boyd-Grinstein-Lebed (BGL) parametrisations of the form factors, and the relevant quantities for both are extracted.