We investigate the effects of an external magnetic field in the gluon dynamics of a color superconductor with three massless quark flavors. In the framework of gluon mean-field theory at asymptotic densities, we show that the long-range component H[over ] of the external magnetic field that penetrates the color-flavor locked phase produces an instability when its strength becomes larger than the Meissner mass of the charged gluons. As a consequence, the magnetic field causes the formation of a vortex state characterized by the condensation of charged gluons and the creation of magnetic flux tubes. Inside the flux tubes, the magnetic field is stronger than the applied one. This antiscreening effect is connected to the anomalous magnetic moment of the gluon field. We suggest how this same mechanism could serve to remove the chromomagnetic instabilities existing in gapless color superconductivity.