The survival of galactic magnetic fields places a limit on the flux of magnetic monopoles, the so-called ''Parker limit.'' Previous discussions of the Parker limit have assumed that the charge of the monopole is the Dirac value, g/sub Dirac/ = 2..pi../e. However, if the grand unified group is broken by Wilson lines, as is assumed in some superstring models, the minimum value of the magnetic charge is not the Dirac quantum, but an integer multiple of it. In this brief report we investigate the dependence of the Parker limit on the charge of the magnetic monopole. 10 refs., 1 fig.