Within a Ginzburg-Landau formalism we establish analytically the necessary and sufficient conditions to realize a doubly degenerate superconducting ground state with broken time-reversal symmetry (BTRS) in a multiband superconductor. Using these results we analyze the ground state of a three-band superconductor in the cylindrical geometry in an external magnetic field. We show that depending on the interband coupling constants, a magnetic flux can induce current density jumps in such superconducting geometries that are related to adiabatic or nonadiabatic transitions from BTRS to time-reversal-symmetric states and vice versa. This unusual current-induced magnetic flux response can in principle be used experimentally to detect superconducting BTRS ground states as well as corresponding metastable excited states.