  From the effects of the Lorentz symmetry violation in the CPT-even gauge
sector of Standard Model Extension, we establish a possible scenario where an
analogue of the He-McKellar-Wilkens effect can stem from. Besides, we build
quantum holonomies associated with the analogue of the He-McKellar-Wilkens
effect and discuss a possible analogy with the holonomic quantum computation
[P. Zanardi and M. Rasetti, Phys. Lett. A {\bf264}, 94 (1999)]. Finally, we
investigate the dependence of the energy levels on the He-McKellar-Wilkens
geometric phase induced by Lorentz symmetry breaking effects when the particle
is confined to a hard-wall confining potential.
