Compact U(1) gauge theory in (3+1)-dimensions possesses the confining phase, characterized by a linear raise of the potential between particles with opposite electric charges at sufficiently large interparticle separation. The confinement phenomenon is generated by condensation of Abelian monopoles at strong gauge coupling. We study the properties of monopoles and the deconfining order parameter in zero-temperature theory in the presence of ideally conducting parallel metallic boundaries (plates) usually associated with the Casimir effect. Using first-principle numerical simulations in compact U(1) lattice gauge theory, we show that as the distance between the plates diminishes, the vacuum in between the plates experiences a deconfining transition. The phase diagram in the space of the gauge coupling and the interplane distance is obtained.