We report on measurements of the time-dependent CP violating observables in $B^0_srightarrow D^{mp}_s K^{pm}$ decays using a dataset corresponding to 1.0 fb$^{-1}$ of pp collisions recorded with the LHCb detector. We find the CP violating observables $C_f=0.53pm0.25pm0.04$, $A^{DeltaGamma}_f=0.37pm0.42pm0.20$, $A^{DeltaGamma}_{bar{f}}=0.20pm0.41pm0.20$, $S_f=-1.09pm0.33pm0.08$, $S_{bar{f}}=-0.36pm0.34pm0.08$, where the uncertainties are statistical and systematic, respectively. Using these observables together with a recent measurement of the $B^0_s$ mixing phase $-2beta_s$ leads to the first extraction of the CKM angle $gamma$ from $B^0_s rightarrow D^{mp}_s K^{pm}$ decays, finding $gamma$ = (115$_{-43}^{+28}$)$^circ$ modulo 180$^circ$ at 68% CL, where the error contains both statistical and systematic uncertainties.