BRUSSELS—European Union regulators confirmed Thursday they have opened a full-blown probe into McDonald’s Corp.’s tax affairs in Luxembourg, warning that a tax deal granted to the fast-food chain in 2009 may have illegally reduced its tax burden.

The move embroils a fourth U.S. multinational in a widening EU tax investigation that is a priority for policy makers in Brussels, but has drawn criticism from the U.S. government.

The European Commission, the bloc’s top antitrust regulator, said it would examine whether a 2009 tax ruling granted to a Luxembourg unit of the restaurant chain, McDonald’s Europe Franchising, had allowed it to avoid paying corporate tax in either Luxembourg or the U.S.

The unit, which collects royalty fees from McDonald’s franchisees across Europe and Russia, has paid no corporate tax in Luxembourg since 2009 despite recording large profits, including more than €250 million in 2013, the commission said.

Tax rulings are routinely used by multinational corporations to provide certainty about their future tax bills, but EU regulators worry they may have been used to allow some companies to underpay tax.