The observation of the $\Lambda_\mathrm{b}^0$ $\to$ J/$\psi \Lambda \phi$ decay is reported using proton-proton collision data collected at $\sqrt{s} =$ 13 TeV by the CMS experiment at the LHC in 2018, corresponding to an integrated luminosity of 60 fb$^{-1}$. The ratio of the branching fractions $\mathcal{B}(\Lambda_\mathrm{b}^0$ $\to$ J/$\psi \Lambda \phi)$ $/$ $\mathcal{B}(\Lambda_\mathrm{b}^0$ $\to$ $\psi \Lambda)$ is measured to be (8.26 $\pm$ 0.90 (stat) $\pm$ 0.68 (syst) $\pm$ 0.11 $(\mathcal{B}))$ $\times$ 10$^{-2}$, where the first uncertainty is statistical, the second is systematic, and the last uncertainty reflects the uncertainties in the world-average branching fractions of $\phi$ and $\psi$(2S) decays to the reconstructed final states.