  The ALICE Collaboration has measured the energy dependence of exclusive
photoproduction of $J/\psi$ vector mesons off proton targets in
ultra-peripheral p-Pb collisions at a centre-of-mass energy per nucleon pair
$\sqrt{s_{\rm NN}} = 5.02$ TeV. The e$^+$e$^-$ and $\mu^+\mu^-$ decay channels
are used to measure the cross section as a function of the rapidity of the
$J/\psi$ in the range $-2.5 < y < 2.7$, corresponding to an energy in the
$\gamma$p centre-of-mass in the interval $40 < W_{\gamma\mathrm{p}}<550$ GeV.
The measurements, which are consistent with a power law dependence of the
exclusive $J/\psi$ photoproduction cross section, are compared to previous
results from HERA and the LHC and to several theoretical models. They are found
to be compatible with previous measurements.
