We show that monopoles can be pair produced by cosmological magnetic fields in the early Universe. The pair production gives rise to relic monopoles and, at the same time, induces a self-screening of the magnetic fields. By studying these effects we derive limits on the monopole mass and also on the initial amplitude of primordial magnetic fields. Monopoles of GUT scale mass can even be produced if primordial magnetic fields exist at sufficiently high redshifts.
