The first measurement of the dependence on $|t|$, the square of the momentum transferred between the incoming and outgoing target nucleus, of coherent J/ψ photoproduction is presented. The data were measured with the ALICE detector in ultra-peripheral Pb-Pb collisions at a centre-of-mass energy per nucleon pair $\sqrt{s_{\rm NN}} = 5.02$ TeV with the J/$\psi$ produced in the central rapidity region $|y| < 0.8$, which corresponds to the small Bjorken-$x$ range $(0.3 − 1.4) \times 10 ^{−3}$. The measured $|t|$-dependence is not described by computations based only on the Pb nuclear form factor, while the photonuclear cross section is better reproduced by models including shadowing according to the leading-twist approximation, or gluon-saturation effects from the impact-parameter dependent Balitsky-Kovchegov equation. This new observable is therefore a valid tool to constrain the relevant model parameters and to investigate the transverse gluonic structure at very low Bjorken-$x$. The first measurement of the cross section for coherent J/ψ photoproduction as a function of |t| , the square of the momentum transferred between the incoming and outgoing target nucleus, is presented. The data were measured with the ALICE detector in ultra-peripheral Pb–Pb collisions at a centre-of-mass energy per nucleon pair sNN=5.02TeV with the J/ψ produced in the central rapidity region |y