BRUSSELS—Representatives from Europe’s struggling steel industry will take to the streets of Brussels on Monday in an attempt to stop the European Union from granting market-economy status to China later this year, a move that would make it harder for European companies to protect themselves from cheap Chinese exports.

The protest by workers and employers follows a stark warning from some of the EU’s largest governments that the bloc’s steel sector faces a significant and impending risk of collapse. It is also likely to fuel...