Effects of external magnetic fields on the criteria of free exciton magnetic polaron (EMP) formation and interface-trapped EMP formation in quantum wells (QWs) with semimagnetic barriers are studied. We found that for the field normal to the QW plane the temperature range of a free EMP formation is limited by two critical temperatures and decreases with increase of the field vanishing at some critical field. Magnetic field parallel to the QW plane also suppresses a free EMP, but in this case there is only one (upper) critical temperature. The interface-trapped EMP formation becomes easier in the field normal to the QW plane, but it is more difficult if the field parallel to the QW plane is applied.