Using a data sample of proton-proton collisions at sqrt[s]=13 TeV, corresponding to an integrated luminosity of 140 fb^{-1} collected by the CMS experiment in 2016-2018, the B_{s}^{0}→X(3872)ϕ decay is observed. Decays into J/ψπ^{+}π^{-} and K^{+}K^{-} are used to reconstruct, respectively, the X(3872) and ϕ. The ratio of the product of branching fractions B[B_{s}^{0}→X(3872)ϕ]B[X(3872)→J/ψπ^{+}π^{-}] to the product B[B_{s}^{0}→ψ(2S)ϕ]B[ψ(2S)→J/ψπ^{+}π^{-}] is measured to be [2.21±0.29(stat)±0.17(syst)]%. The ratio B[B_{s}^{0}→X(3872)ϕ]/B[B^{0}→X(3872)K^{0}] is found to be consistent with one, while the ratio B[B_{s}^{0}→X(3872)ϕ]/B[B^{+}→X(3872)K^{+}] is two times smaller. This suggests a difference in the production dynamics of the X(3872) in B^{0} and B_{s}^{0} meson decays compared to B^{+}. The reported observation may shed new light on the nature of the X(3872) particle.