  We compute the leading-logarithmic correction to the neutrino mass matrix in
the Standard Model effective field theory (SMEFT) to dimension seven. In the
limit of negligible lepton and down-type quark Yukawa couplings, it receives
contributions from the Weinberg dimension-five operator as well as from 11
dimension-six and five dimension-seven independent interactions. Two of the
main implications we derive from this result are the following. First, we find
dimension-seven operators which, despite violating lepton number, do not
renormalise neutrino masses at one loop. And second, we demonstrate that the
presence of dimension-six operators around the TeV scale can modify the
Standard Model prediction by up to $\mathcal{O}(50\,\%)$. Our result comprises
also one step forward towards the renormalisation of the SMEFT to order
$v^3/\Lambda^3$.
