From an analysis of the flavor-tagged decay ${B}_{s}^{0}\ensuremath{\rightarrow}J/\ensuremath{\psi}\ensuremath{\phi}$ we obtain the width difference between the ${B}_{s}^{0}$ light and heavy mass eigenstates, $\ensuremath{\Delta}{\ensuremath{\Gamma}}_{s}=0.19\ifmmode\pm\else\textpm\fi{}0.07(\mathrm{stat}{)}_{\ensuremath{-}0.01}^{+0.02}(\mathrm{syst})\text{ }\text{ }{\mathrm{ps}}^{\ensuremath{-}1}$, and the $CP$-violating phase, ${\ensuremath{\phi}}_{s}=\ensuremath{-}{0.57}_{\ensuremath{-}0.30}^{+0.24}(\mathrm{stat}{)}_{\ensuremath{-}0.02}^{+0.08}(\mathrm{syst})$. The allowed 90% CL intervals of $\ensuremath{\Delta}{\ensuremath{\Gamma}}_{s}$ and ${\ensuremath{\phi}}_{s}$ are $0.06<\ensuremath{\Delta}{\ensuremath{\Gamma}}_{s}<0.30\text{ }\text{ }{\mathrm{ps}}^{\ensuremath{-}1}$ and $\ensuremath{-}1.20<{\ensuremath{\phi}}_{s}<0.06$, respectively. The data sample corresponds to an integrated luminosity of $2.8\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ accumulated with the D0 detector at the Fermilab Tevatron collider.