A search for the rare decay $B0\to J/\psi \varphi$ is performed using $pp$ collision data collected with the LHCb detector at centre-of-mass energies of 7, 8 and 13 TeV, corresponding to an integrated luminosity of 9 $fb-1$. No significant signal of the decay is observed and an upper limit of $1.1\times 10-7$ at 90% confidence level is set on the branching fraction.