A search for the decay $B0\to \varphi \mu +\mu -$ is performed using proton-proton collisions at centre-of-mass energies of 7, 8, and 13 TeV collected by the LHCb experiment and corresponding to an integrated luminosity of 9 fb$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$. No evidence for the $B0\to \varphi \mu +\mu -$ decay is found and an upper limit on the branching fraction, excluding the $\varphi$ and charmonium regions in the dimuon spectrum, of $4.4\times 10-3$ at a 90$\%$ credibility level, relative to that of the $Bs0\to \varphi \mu +\mu -$ decay, is established. Using the measured $Bs0\to \varphi \mu +\mu -$ branching fraction and assuming a phase-space model, the absolute branching fraction of the decay $B0\to \varphi \mu +\mu -$ in the full $q2$ range is determined to be less than $3.2\times 10-9$ at a 90$\%$ credibility level.