A search for the rare decay of a B0 or B0s meson into the final state J/ψγ is performed, using data collected by the LHCb experiment in pp collisions at s√=7 and 8 TeV, corresponding to an integrated luminosity of 3  fb−1. The observed number of signal candidates is consistent with a background-only hypothesis. Branching fraction values larger than 1.5×10−6 for the B0→J/ψγ decay mode are excluded at 90% confidence level. For the B0s→J/ψγ decay mode, branching fraction values larger than 7.3×10−6 are excluded at 90% confidence level; this is the first branching fraction limit for this decay.