The antimagic field spell "suppresses any spell or magical effect used within, brought into, or cast into the area". Also, "a magic sword does not function magically within the area". Since curses are magical in nature, they are supressed when brought within the confines of the field. Thus, you can take off cursed magic items by walking into an antimagic field.
As a note of comparison, remove curse, the normal way of removing cursed items, is only 3rd level, while antimagic field is 6th, so this isn't even a stretch power-wise.