We calculate the quarkonium dissociation rate in the P and CP-odd domains (bubbles) that were possibly created in heavy-ion collisions. In the presence of the magnetic field produced by the valence quarks of colliding ions, parity-odd domains generate electric field. Quarkonium dissociation is the result of quantum tunneling of quark or antiquark through the potential barrier in this electric field. The strength of the electric field in the quarkonium comoving frame depends on the quarkonium velocity with respect to the background magnetic field. We investigate momentum, electric field strength and azimuthal dependence of the dissociation rate. Azimuthal distribution of quarkonia surviving in the electromagnetic field is strongly anisotropic; the form of anisotropy depends on the relation between the electric and magnetic fields and quarkonium momentum P⊥. These features can be used to explore the properties of the electromagnetic field created in heavy ion collisions.