The ${B}_{s}^{0}$ differential production cross section is measured as functions of the transverse momentum and rapidity in $pp$ collisions at $\sqrt{s}=7\text{ }\text{ }\mathrm{TeV}$, using the ${B}_{s}^{0}\ensuremath{\rightarrow}J/\ensuremath{\psi}\ensuremath{\phi}$ decay, and compared with predictions based on perturbative QCD calculations at next-to-leading order. The data sample, collected by the CMS experiment at the LHC, corresponds to an integrated luminosity of $40\text{ }\text{ }{\mathrm{pb}}^{\ensuremath{-}1}$. The ${B}_{s}^{0}$ is reconstructed from the decays $J/\ensuremath{\psi}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ and $\ensuremath{\phi}\ensuremath{\rightarrow}{K}^{+}{K}^{\ensuremath{-}}$. The integrated ${B}_{s}^{0}$ cross section times ${B}_{s}^{0}\ensuremath{\rightarrow}J/\ensuremath{\psi}\ensuremath{\phi}$ branching fraction in the range $8<{p}_{\mathrm{T}}^{B}<50\text{ }\text{ }\mathrm{GeV}/c$ and $|{y}^{B}|<2.4$ is measured to be $6.9\ifmmode\pm\else\textpm\fi{}0.6\ifmmode\pm\else\textpm\fi{}0.6\text{ }\text{ }\mathrm{nb}$, where the first uncertainty is statistical and the second is systematic.