  Spatially non-local matrix elements are useful lattice-QCD observables in a
variety of contexts, for example in determining hadron structure. To quote
credible estimates of the systematic uncertainties in these calculations, one
must understand, among other things, the size of the finite-volume effects when
such matrix elements are extracted from numerical lattice calculations. In this
work, we estimate finite-volume effects for matrix elements of non-local
operators, composed of two currents displaced in a spatial direction by a
distance $\xi$. We find that the finite-volume corrections depend on the
details of the matrix element. If the external state is the lightest degree of
freedom in the theory, e.g.~the pion in QCD, then the volume corrections scale
as $ e^{-m_\pi (L- \xi)} $, where $m_\pi$ is the mass of the light state. For
heavier external states the usual $e^{- m_\pi L}$ form is recovered, but with a
polynomial prefactor of the form $L^m/|L - \xi|^n$ that can lead to enhanced
volume effects. These observations are potentially relevant to a wide variety
of observables being studied using lattice QCD, including parton distribution
functions, double-beta-decay and Compton-scattering matrix elements, and
long-range weak matrix elements.
