In this paper, we present the branching ratio and polarization fraction of two body decay of $B_s^0$ to the vector mesons $\varphi \left(1020\right)$ and $X\left(3872\right)$ in which the $X\left(3872\right)$ meson can be considered as an intermediate resonance in the final decay $B_s^0\to J/\psi {\pi }^{+}{\pi }^{-}\varphi \left(1020\right)$. For this aim, the naive factorization approach is used to calculate the decay amplitude with the different helicities due to the combination of polarization states of two mesons $X\left(3872\right)$ and $\varphi \left(1020\right)$. Within the framework of the factorization approach, we find the branching fraction for the two body channel of $B_s^0\to X\left(3872\right)\varphi \left(1020\right)=(6.31\pm 0.01)\times {10}^{-5}$ and also $Br\left(X\right(3872)\to J/\psi {\pi }^{+}{\pi }^{-})$ and $Br\left(X\right(3872)\to J/\psi {\pi }^{+}{\pi }^{-})Br(B_s^0\to X(3872\left)\varphi \right(1020\left)\right)$ are calculated which are in well agreement with CMS collaboration data. Furthermore, we estimate the decay width of resonance $X\left(3872\right)$ into final states $J/\psi {\pi }^{+}{\pi }^{-}$ which is within the range of experimental data. By these results and available experimental data, we render the branching ratio of decays $B^{+}$ and $B_s^0$ into $X\left(3872\right)K^{+}$ and $X\left(3872\right)K^0$, respectively. Also, in the nonleptonic two body decay of $B_s^0\to X\left(3872\right)\varphi \left(1020\right)$, the direct and indirect CP-violating asymmetries are estimated to indicate the potential role of the such decays to measure CP-violation.